42 (number)

42 (forty-two) is the natural number that follows 41 and precedes 43.

Mathematics

Forty-two (42) is the sixth pronic number^[1] and the eighth abundant number,^[2] with an abundance of 12,^[3] equal to the average of its eight divisors as an arithmetic number.^[4][5]

Its

${\displaystyle 2\times 3\times 7}$

It is also the sum of the first six positive non-zero even numbers, ${\displaystyle 2+4+6+8+10+12}$, and a Harshad number in decimal, because the sum of its digits is six ${\displaystyle (4+2=6)}$, which

42 is the fifth Catalan number, following 14; consequently, it is^[9]

Additionally, 42 is the smallest number ${\displaystyle k}$ that is equal to the sum its non-prime

${\displaystyle 42=1+6+14+21}$

42 is also the third primary pseudoperfect number,^[12] and the first (2,6)-perfect number (super-multiperfect), where ${\displaystyle \sigma ^{2}(n)=\sigma (\sigma (n))=6n.}$^[13]

42 is the number of integer partition of 10: the number of ways of expressing 10 as a sum of positive integers.^[14] 1111123, one of the forty-two unordered integer partitions of 10, has 42 ordered compositions, since ${\displaystyle 7!\div 5!=42.}$

As a polygonal number, 42 is the first (non-trivial) fifteen-sided pentadecagonal number.^[15] It is also the fourth meandric number,^[16] and seventh open meandric number^[17] (following 8 and 14, respectively).

On the other hand, an angle of 42 degrees can be constructed with a

Where the

42 is also the first non-trivial hendecagonal (11-gonal) pyramidal number, after 12.^[21][22][a] Otherwise, forty-two is the least possible number of diagonals of a simple convex hendecahedron (or 11-faced polyhedron).^[28][29][b]

42 is the only known ${\displaystyle k}$ that is equal to the number of sets of four distinct positive integers ${\displaystyle (a,b,c,d)}$ — each less than ${\displaystyle k}$ — such that ${\displaystyle {\text{ }}ab-cd,{\text{ }}}$ ${\displaystyle ac-bd{\text{ }}}$ and ${\displaystyle {\text{ }}ad-bc{\text{ }}}$ are all multiples of ${\displaystyle k}$. Whether there are other values remains an open question.^[30]

42 is the resulting number of the original Smith number: ${\displaystyle 4937775=3\times 5\times 5\times 65837.}$ Both the sum of its digits, ${\displaystyle 4+9+3+7+7+7+5}$, and the sum of the digits in its prime factorization, ${\displaystyle 3+5+5+(6+5+8+3+7)}$, result in 42.^[31]

42 is the number of isomorphism classes of all simple and oriented directed graphs on four vertices.^[32] I.e., the number of all outcomes (up to isomorphism) of a tournament of four teams where a game between a pair of teams results in three possible outcomes: wins from either team, or a draw.^[33]

42 is the fourth Robbins number, equivalently the number of ${\displaystyle 4\times 4}$ alternating sign matrices.^[34][35] It is also the number of ways to arrange the numbers ${\displaystyle 1}$ through ${\displaystyle 9}$ in a ${\displaystyle 3\times 3}$ matrix such that the numbers in each row and column are in ascending order.

42 is the magic constant of the smallest non-trivial magic cube, a ${\displaystyle 3\times 3\times 3}$ cube with entries of 1 through 27, where every row, column, corridor, and diagonal passing through the center sums to forty-two.^[36][37]

42 is the number of (3, 3, 3) standard Young tableaux that use distinct entries^[38][39][40] (as well as the number of (2, 2, 2, 2, 2) tableaux).^[41][42]

The last natural number less than

$${\displaystyle 80,435,758,145,817,515^{3}+12,602,123,297,335,631^{3}+(-80,538,738,812,075,974)^{3}=42.}$$

The dimension of the Borel subalgebra in the exceptional Lie algebra e₆ is 42.

42 is the smallest number ${\displaystyle k}$ such that for every Riemann surface ${\displaystyle \mathbf {C} }$ of genus ${\displaystyle g\geq 2}$, ${\displaystyle \#{\text{Aut}}(C)\leq k\ {\text{deg}}(K_{C})=k(2g-2)}$ (by the Hurwitz's automorphisms theorem).

This is related to 42 being the largest ${\displaystyle n}$ where there exist positive integers ${\displaystyle p,q,r}$ whose reciprocals alongside that of forty-two generate the sum,^[44]

$${\displaystyle 1={\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{42}}.}$$

Notice that the first three unit fractions are the first values in the infinite series (of Egyptian fractions) that most rapidly converges to ${\displaystyle 1}$ (see, Sylvester's sequence).

Other properties

42 is the smallest integer that can only be made from a minimal number of fours (seven) using only addition, subtraction, multiplication, and division, where an intermediate value has to be a non-integer:^{[citation needed]}

${\displaystyle 42=(4+4)\times (4+{\frac {4+{\frac {4}{4}}}{4}})=8\times 5.25.}$

In decimal representation, the first three digits of pi, ${\displaystyle 3.14\ldots \approx \pi }$, can be arranged as a set of two strings to yield: ${\displaystyle 3\times 14=42.}$

In the terminating decimal of the approximation for pi, the string ${\displaystyle 42\;42\;42}$ occurs at the 242424th decimal "position" (when treating the

• 42 is the atomic number of molybdenum.
• 42 is the atomic mass of one of the naturally occurring stable isotopes of calcium.
• The angle rounded to whole degrees for which a
  rainbow
  appears (the critical angle).
• In 1966, mathematician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the
  Sylvie and Bruno Concluded.^[49]) Now we know that is inaccurate, and it only would take about 38 minutes.^[50]
• As determined by the Babylonians, in 79 years, Mars orbits the Sun almost exactly 42 times.[51]
• The hypothetical efficiency of converting mass to energy, as per ${\displaystyle E=mc^{2},}$ by having a given mass orbit a rotating black hole, is 42%, the highest efficiency yet known to modern physics.^[52]
• In Powers of Ten by Ray and Charles Eames, the known universe from large-scale to small-scale is represented by 42 different powers of ten. These powers range from 10²⁵ meters to 10⁻¹⁷ meters.

Technology

• Magic numbers used by programmers:
  • In
    word
    of every file is 42, "an arbitrary but carefully chosen number that further identifies the file as a TIFF file".
  • In the reiser4 file system, 42 is the inode number of the root directory.
  • In the military IRIG 106 Chapter 10^[53] data recording standard, the hex value 0x464F52545974776F (ASCII "FORTYtwo") is used as a magic number to identify directory blocks.
• The
  binary pattern 00101010 (42) as an XOR cipher
  .
• Tiling a plane using regular hexagons, which is honeycomb in appearance, is approximated in a topological sense to an accuracy of better than 1% using a stretcher bond brick pattern with bricks of 42 squares (6 by 7).^[54]
• The password expiration policy for a Microsoft Windows domain defaults to 42 days.^[55]
• The ASCII code 42 is for the asterisk symbol, being a wildcard for everything.

Astronomy

• diffuse nebula in the constellation Orion, also known as the Orion Nebula
  .
• The New General Catalogue object NGC 42, a spiral galaxy in the constellation Pegasus.
• In January 2004, asteroid 2001 DA₄₂ was given the permanent name 25924 Douglasadams, for the author Douglas Adams who popularized the number 42. Adams died in 2001. Brian G. Marsden, the director of the Minor Planet Center and the secretary for the naming committee, remarked that, with even his initials in the provisional designation, "This was sort of made for him, wasn't it?".
• exoplanets
  found to date.
• main-belt asteroid
  measuring about 100 km in diameter.

• Ancient Egyptian religion: Over most of pharaonic Egyptian history, the empire was divided into 42 nomes. Ancient Egyptian religion and mythological structure frequently model this terrestrial structure.^[56]
  • 42 body parts of Osiris: In some traditions of the Osiris myth, Seth slays Osiris and distributes his 42 body parts all over Egypt. (In others, the number is fourteen and sixteen).^[57]
  • 42 negative confessions: In Ancient Egyptian religion, the 42 negative confessions were a list of questions asked of deceased persons making their journey through the underworld after death.
    Ma'at was an abstract concept representing moral law, order, and truth in both the physical and moral spheres, as well as being an important goddess in the religion. In the judgment scene described in the Egyptian Book of the Dead, which evolved from the Coffin Texts and the Pyramid Texts, 42 questions were asked of the deceased person as part of the assessment of Ma'at. If the deceased person could reasonably give answers to the 42 questions, they would be permitted to enter the afterlife. These 42 questions are known as the "42 Negative Confessions" and can be found in funerary texts such as the Papyrus of Ani
    .
  • 42 books in the core library: Clement of Alexandria states that the Egyptian temple library is divided into 42 "absolutely necessary" books that formed the stock of a core library. 36 contain the entire philosophy of the Egyptians which are memorized by the priests. While the remaining 6, are learned by the Pastophoroi (image-bearers).[58]^[59] (36 is like-wise a sacred number in Egyptian thought, related to time, in particular the thirty-six Decan stars and the thirty-six, 10-day "weeks" in the Egyptian year.^[60]) The 42 books were not canonized like the Hebrew bible; they only supported and never replaced temple ritual. Hence, the destruction of the Egyptian temples and the cessation of the rituals ended Egyptian cultural continuity.^[61]
• Abrahamic religions
  • There are 42
    Deuteronomy
    .
  • In 2 Kings 2:24, the she-bears summoned by Elisha kill forty-two boys.
  • In Judaism, the number (in the Babylonian Talmud, compiled 375 AD to 499 AD) of the "Forty-Two Lettered Name" ascribed to God. Rab (or Rabhs), a 3rd-century source in the Talmud stated "The Forty-Two Lettered Name is entrusted only to him who is pious, meek, middle-aged, free from bad temper, sober, and not insistent on his rights". [Source: Talmud Kidduschin 71a, Translated by Rabbi I. Epstein]. Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names [Maimonides "Moreh"]. The apparently unpronouncable Tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Two Lettered Name of the Talmud.^{[citation needed]}
  • In
    Sefer Torah
    ).
  • 42 is the number with which God creates the Universe in
    Sephirot").^[64] The Forty-Two-Lettered Name contains four combined names which are spelled in Hebrew letters (spelled in letters = 42 letters), which is the name of Azilut (or "Atziluth
    " "Emanation"). While there are obvious links between the Forty-Two Lettered Name of the Babylonian Talmud and the Kabbalah's Forty-Two Lettered Name, they are probably not identical because of the Kabbalah's emphasis on numbers. The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.
  • The number 42 appears in various contexts in
    Revelation 14:7
    )→ 1,000 years per day/24 hours per day ≈ 42 years/hour, etc.
  • The Gutenberg Bible is also known as the "42-line Bible", as the book contained 42 lines per page.
  • The
    Forty-Two Articles (1552), largely the work of Thomas Cranmer, were intended to summarize Anglican doctrine, as it now existed under the reign of Edward VI
    .
• East Asian religions
  • The
    Sutra of Forty-two Sections
    is a Buddhist scripture.
  • In Japanese culture, the number 42 is considered unlucky because the numerals when pronounced separately—shi ni (four two)—sound like the word "dying",^[65] like the Latin word "mori".

Popular culture

The Hitchhiker's Guide to the Galaxy

The number 42 is, in

.

The fourth book in the series, the novel So Long, and Thanks for All the Fish, contains 42 chapters. According to the novel Mostly Harmless, 42 is the street address of Stavromula Beta. In 1994, Adams created the

42 Puzzle, a game based on the number 42. Adams says he picked the number

simply as a joke, with no deeper meaning.

easter egg when one searches "the answer to the ultimate question of life, the universe, and everything." Once typed (all in lowercase), the calculator answers with the number 42.^[67]

In Hervé Le Tellier's novel The Anomaly, a top-secret US Government protocol receives code number 42, inspired by this source.^{[citation needed]}

Works of Lewis Carroll

Lewis Carroll, who was a mathematician,^[68] made repeated use of this number in his writings.^[69]

Examples of Carroll's use of 42:

• Alice's Adventures in Wonderland has 42 illustrations.
• Alice's attempts at multiplication (chapter two of Alice in Wonderland) work if one uses base 18 to write the first answer, and increases the base by threes to 21, 24, etc. (the answers working up to 4 × 12 = "19" in base 39), but "breaks" precisely when one attempts the answer to 4 × 13 in base 42, leading Alice to declare "oh dear! I shall never get to twenty at that rate!"^{[citation needed]}
• Rule Forty-two in Alice's Adventures in Wonderland ("All persons more than a mile high to leave the court").
• Rule 42 of the Code in the preface^[70] to The Hunting of the Snark ("No one shall speak to the Man at the Helm").
• In "fit the first" of The Hunting of the Snark the Baker had "forty-two boxes, all carefully packed, With his name painted clearly on each."^[71]
• The White Queen announces her age as "one hundred and one, five months and a day", which—if the best possible date is assumed for the action of Through the Looking-Glass (e.g., a date is chosen such that the rollover from February to March is excluded from what would otherwise be an imprecise measurement of "five months and a day")—gives a total of 37,044 days. If the Red Queen, as part of the same chess set, is regarded as the same age, their combined age is 74,088 days, or 42 × 42 × 42.^[72]

Music

• 42 Dugg is an American rapper.
• "Forty-two" ("42") is a work (dedicated to Elvis Presley, Joe Dassin and Vladimir Vysotsky) for oboe and symphony orchestra by Estonian composer Peeter Vähi.
• funk
  music band.
• "42" is one of the tracks on Coldplay′s 2008 album Viva la Vida or Death and All His Friends.
• "
  Channel 42" is an electronic music song by deadmau5 featuring Wolfgang Gartner; it appears on the 2012 deadmau5 album Album Title Goes Here
  .
• "42" is a song from Mumford and Sons′ 2018 album Delta.
• "42" is a song written and produced by hip-hop and record production trio
  Seo Changbin of popular k-pop group Stray Kids. A lyric in this song states, "Why do we live? What's the purpose? Is it 42? Stop speaking nonsense," which directly references The Hitchhiker's Guide to the Galaxy
  's definition of 42.
• ""42"" is a song from the 2018 album SR3MM by American rap duo Rae Sremmurd.
• "42" is a song from the 2019 album Don′t Panic by the progressive rock band IZZ. The album is a partial concept album based on The Hitchhiker's Guide to the Galaxy.
• "42" is a song by
  The Disco Biscuits.^[73]

Television and film

• The Kumars at No. 42 is a British comedy television series.
• "42" is an episode of Doctor Who, set in real time lasting approximately 42 minutes.
• On the game show
  Watson" the IBM supercomputer has 42 "threads" in its avatar.^[74]
• 42 is a film on the life of American baseball player Jackie Robinson.
• Captain Harlock is sometimes seen wearing clothing with the number 42 on it.
• In the
  Stargate Atlantis season 4
  episode "Quarantine", Colonel Sheppard states that Dr. McKay's password ends in 42 because "It's the ultimate answer to the great question of life, the universe and everything."
• In
  sum of three cubes.^[43]
• In the TV show Lost, 42 is one of the numbers used throughout the show for some of its mysteries.
• There is a Belgian TV drama called Unit 42 about a special police unit that uses high-tech tools to go after criminals. One of the characters in the pilot episode explains that the unit was named based on the Hitchhiker's Guide.

Video games

• 42 Entertainment is the company responsible for several alternate reality games, including I Love Bees, Year Zero, and Why So Serious.
• Tokyo 42 is a video game released in 2017.
• Squadron 42
  is a video game set in the Star Citizen Universe with an unspecified release date.

Sports

• The
  jersey number of Jackie Robinson, which is the only number retired by all Major League Baseball teams. Although the number was retired in 1997, Mariano Rivera of the New York Yankees, the last professional baseball player to wear number 42, continued to wear it until he retired at the end of the 2013 season. As of the 2014 season, no player ever again wore the number 42 in Major League Baseball except on Jackie Robinson Day
  (April 15), when all uniformed personnel (players, managers, coaches, and umpires) wear the number.
• The number of the
  laws of cricket.^[76]
• Rule 42 is the historic name of a Gaelic Athletic Association rule (now codified in Rule 5.1 and Rule 44) that in practice prohibits the playing of "foreign sports" (generally association football and the rugby codes) at GAA grounds.

Architecture

• The architects of the Rockefeller Center in New York City worked daily in the Graybar Building where on "the twenty-fifth floor, one enormous drafting room contained forty-two identical drawing boards, each the size of a six-seat dining room table; another room harboured twelve more, and an additional fourteen stood just outside the principals' offices at the top of the circular iron staircase connecting 25 to 26".^[77]
• In the Rockefeller Center (New York City) there are a total of "forty-two elevators in five separate banks"^[78] which carry tenants and visitors to the sixty-six floors.

Comics

• Miles Morales was bitten by a spider bearing the number 42, causing him to become a Spider-Man. The number was later heavily referenced in the film Spider-Man: Into the Spider-Verse. The use of 42 within the franchise references Jackie Robinson's use of the number, though many fans incorrectly believed it to be a Hitchhiker's Guide to the Galaxy reference.^[79]

Other fields

• +42 is the historical Select Country for the former country of Czechoslovakia.
• There are 42 US gallons in a barrel of oil.
• 42 is the number of the French department of Loire. The number is also reflected in the postal code for that area.
• NatWest Tower.^[80]
• In New York City, 42nd Street is a main and very popular two-way thoroughfare. Landmarks on it include the Chrysler Building, Grand Central Terminal, the main branch of the New York Public Library, and Times Square. The Headquarters of the United Nations is at the east end of the street. The New York City street is also the setting for a movie by the same name (which also gave fame to its eponymous title song), and which later inspired a musical adaptation, 42nd Street.
• 42 is the inspiration for the name of the 42 Center of Excellence for Artificial Intelligence, based in Vienna, Austria.^[81]
• 42 is the name of the private
  Paris, France, and Fremont, California
  .
• 42 in Chinese reads sì èr, which is very close to shì a (是啊), which means 'yes'. It was once popular among young Chinese to send '42' as a short message to stand for 'yes'.^[citation needed]
• 42 is the sum of the numbers on a pair of dice.
• 42 (dominoes) is a trick-taking game played with dominoes, rather than cards. Originated and predominantly found in Texas.
• 42 is the number of times a standard sheet of paper would need to be folded over onto itself for the thickness of the folded piece of paper to be thick enough to reach the Moon from the surface of the Earth.^[82]
• 42 is the maximum amount of marks in the International Mathematical Olympiad.

Other languages

Language	Translation
Afrikaans	twee-en-veertig
Albanian	dyzetedy
Arabic	إثنان و أربعون (ʾithnān wa ʾarbaʿūn)
Armenian	քառասուներկու (karasunerku)
Armenian (Classic)	ԽԲ (khe ben)
Basque	berrogeita bi
Bangla	biyallis ৪২ বিয়াল্লিশ
Belarusian	сорак два (sorak dva)
Bosnian	četrdeset dva
Bulgarian	четиридесет и две (četirideset i dve)
Catalan	quaranta-dos
Chinese	四十二 (肆拾贰) (sìshí'èr)
Chuvash	хĕрĕх иккĕ (xĕrĕx ikkĕ, IIXXXX)
Croatian	četrdeset dva
Czech	čtyřicet dva
Danish	toogfyrre
Dhivehi	Saalhees Dheyh
Dutch	tweeënveertig
Esperanto	kvardek du
Estonian	nelikümmend kaks
Finnish	neljäkymmentäkaksi
Filipino	apatnapu't dalawa
French	quarante-deux
West Frisian	twaenfjirtich
Galician	corenta e dous
Georgian	ორმოცდაორი (ormocdaori)
German	zweiundvierzig
Greek	σαράντα δύο (saránta dýo)
Gujarati	betalis
Hebrew	ארבעים ושתיים (arbayim u-shtayim)
Hindi	बयालीस, ४२ (bayālīs)
Hungarian	negyvenkettő
Icelandic	fjörutíu og tveir
Indonesian	empat puluh dua
Irish	daichead a dó
Italian	quarantadue
Japanese	四十二 (よんじゅうに) (yonjūni)
Kazakh	қырық екі (qırıq eki)
Korean	사십이 / 마흔둘 (sasibi/maheundul)
Kannada	ನಲವತ್ತು ಎರಡು (nalavatthu eradu)
Latin	quadraginta duo
Latvian	četrdesmit divi
Livonian	nēļakimdõ kakš
Lithuanian	keturiasdešimt du
Lojban	vore
Luxembourgish	zweeavéierzeg
Macedonian	четириесет и два (četirieset i dva)
Malayalam	നാല്പത്തിരണ്ടു
Maltese	tnejn u erbgħin
Māori	whā tekau ma rua
Marathi	bechalis
Mongolian	дөчин хоёр (döchin khoyor)
Norwegian	førtito
Pashto	دوه څلوېښت
Persian	چهل و دو (chehel o du)
Polish	czterdzieści dwa
Portuguese	quarenta e dois
Romanian	patruzeci și doi
Russian	сорок два (sorok dva)
Sanskrit	द्विचत्वारिंशत्, ४२ (dvicatvāriṃśat)
Serbian	четрдесет два (četrdeset dva)
Shona	Makumi mana nemaviri
Sinhala	හතලිස් දෙක (hathalis deka)
Slovene	dvainštirideset
Slovak	štyridsaťdva
Somali	laba iyo afartan
Spanish	cuarenta y dos
Swedish	fyrtiotvå
Tagalog	apatnapu't dalawa
Tamil	நாற்பத்திரண்டு (narpatti errundu)
Telugu	నలభై రెండు (nalabai rendu)
Thai	สี่สิบสอง
Turkish	kırk iki
Ukrainian	сорок два (sorok dva)
Urdu	بیالیس (bayālīs)
Vietnamese	bốn mươi hai
Volapük	foldegtel
Welsh	pedwar deg dau / dau-ar-ddeugain
Yoruba	mejilelogoji

See also

• List of highways numbered 42

Notes

1. ^ The eleventh triangular number is 66 (and sixth hexagonal number),^[11][23] that is also the third sphenic number, following 42 and 30.^[6] These first three sphenic numbers are also consecutive (fifth, sixth, and seventh) members in Lemming's simulation sequence, where opposing triangles (starting with just one) are successively joined at vertices (without overlaps in the interior); in this sequence, values represent the total number of triangles joined at each generational step.^[24][25] The sum of these three terms 30 + 42 + 66 = 138, which is the ninth term.
   Where 42 is the twenty-eighth composite number,^[26] the number of integer partitions of the twenty-eighth 28-gonal pyramidal number into distinct 28-gonal pyramidal numbers is 42.^[27]
2. ^ The sequence of minimum diagonals by such ${\displaystyle n}$-faced polyhedra follows the sequence of pronic numbers, whose indexes start with 4 (for a square), rather than 0.^[29][1]

References

1. ^ ^{a b} Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
3. ^ Sloane, N. J. A. (ed.). "Sequence A033880 (Abundance of n, or (sum of divisors of n) - 2n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
4. ^ Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j)).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-08.
5. ^ Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-08.
6. ^ ^{a b} Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
7. ^ Sloane, N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-08.
8. ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
9. ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
10. ^ Sloane, N. J. A. (ed.). "Sequence A331805 (Integers k such that k is equal to the sum of the nonprime proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
11. ^ ^{a b} Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2) equal to n*(n+1)/2 or 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
12. ^ Sloane, N. J. A. (ed.). "Sequence A054377 (Primary pseudoperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
13. ^ Sloane, N. J. A. (ed.). "Sequence A019283 (Let sigma_m (n) be result of applying sum-of-divisors function m times to n; ... (m,k)-perfect if ...; sequence gives the (2,6)-perfect numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
14. ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
15. ^ Sloane, N. J. A. (ed.). "Sequence A051867 (15-gonal (or pentadecagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
16. ^ Sloane, N. J. A. (ed.). "Sequence A005315 (Closed meandric numbers (or meanders): number of ways a loop can cross a road 2n times.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
17. ^ Sloane, N. J. A. (ed.). "Sequence A005316 (Meandric numbers: number of ways a river can cross a road n times.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
18. Zbl 0385.51006
    .
19. ^ Dallas, Elmslie William (1855). "Part II. (VII): Of the Circle, with its Inscribed and Circumscribed Figures − Equal Division and the Construction of Polygons". The Elements of Plane Practical Geometry. London: John W. Parker & Son, West Strand. p. 134.
20. ^ Jardine, Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling.
21. Zbl 1258.11001
    .
    Table for m-gonal pyramidal numbers with 3 ≤ m ≤ 30.
22. ^ Sloane, N. J. A. (ed.). "Sequence A007586 (11-gonal (or hendecagonal) pyramidal numbers: n*(n+1)*(3*n-2)/2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-10.
23. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers: a(n) equal to n*(2*n-1).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-10.
24. JSTOR 30211270 – via OEIS
    .
25. ^ Sloane, N. J. A. (ed.). "Sequence A061776 (Start with a single triangle; at n-th generation add a triangle at each vertex, allowing triangles to overlap; sequence gives number of triangles in n-th generation.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-10.
26. ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-10.
27. ^ Sloane, N. J. A. (ed.). "Sequence A337798 (Number of partitions of the n-th n-gonal pyramidal number into distinct n-gonal pyramidal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-10.
28. Zbl 0948.52003
    .
29. ^ ^{a b} Sloane, N. J. A. (ed.). "Sequence A279019 (Least possible number of diagonals of simple convex polyhedron with n faces.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
30. ^ Kevin Brown. "Differently Perfect". MathPages.
31. OCLC 54611248
    .
32. Zbl 1496.05086
    .
33. Zbl 1489.05075
    .
34. ^ Sloane, N. J. A. (ed.). "Sequence A005130 (Robbins numbers: a(n) is Product_{k equal to 0..n-1} (3k+1)!/(n+k)!; also the number of descending plane partitions whose parts do not exceed n; also the number of n X n alternating sign matrices (ASM's).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
35. ^ Sloane, N. J. A. (ed.). "Sequence A297622 (Triangle read by rows: a(n,k) is the number of k X n matrices which are the first k rows of an alternating sign matrix of size n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
36. Zbl 1003.05500
    .
37. ^ Sloane, N. J. A. (ed.). "Sequence A027441 (a(n) equal to (n^4 + n)/2 (Row sums of an n X n X n magic cube, when it exists).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
38. ^ Sloane, N. J. A. (ed.). "Sequence A005789 (3-dimensional Catalan numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
39. ^ Arndt, Joerg. Sloane, N. J. A. (ed.). "The a(3)=42 Young tableaux of shape [3,3,3]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
40. Mathematical Sciences Research Institute: Numberphile
    . Event occurs at 03:12 − 06:53. Retrieved 2024-01-07.
41. ^ Sloane, N. J. A. (ed.). "Sequence A005791 (5-dimensional Catalan numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-07.
42. Zbl 0398.05008
    .
43. ^
    PMID 33692126
    .
44. UC Riverside
    . Retrieved 2024-01-07.
45. ^ Dave Andersen. "The Pi-Search Page". angio.net. Retrieved 2024-02-09.

    The Meaning of Life (42) and Pi

    "(Quoting from Scott Glazer): Trying to come up with a significant number to search for, I thought of 42 (the answer to life, the universe, and everything in Hitchhikers's Guide to the Galaxy.) 42 would be way too common of course, so I went for 424242. Came back that this shows up at position 242423. Add one (for the decimal point, I lamely rationalize here) and you get 242424, the reverse of the original input. Now that's meaningful... or something.

    "[Editors Note] Amusingly enough, the entire string returned is 242424242. If you disregard either of the ending twos, you find that it's the same position at which you find 42424242. Ahh, the palindromic possibilities inherent in a reversible meaning of life string."

46. doi:10.1119/1.1972773
    .
47. ^ "To Everywhere in 42 Minutes". Time. February 11, 1966. Archived from the original on 12 May 2008. Retrieved 2008-05-18.
48. ^ "Jumping into a 7,965 mile deep hole". YouTube. Archived from the original on June 2, 2008. Retrieved 2008-05-18.
49. Sylvie and Bruno Concluded. Vol. 2. illustrated by Harry Furniss
    . United Kingdom: Macmillan and Co. Each railway is in a long tunnel, perfectly straight: so of course the middle of it is nearer the centre of the globe than the two ends: so every train runs half-way down-hill, and that gives it force enough to run the other half up-hill.
50. ^ Choi, Charles Q. (March 31, 2015). "How Long Would It Take to Fall Through the Earth?". livescience.com. Retrieved 2021-06-27.
51. ^ Powell, Martin J. "Ancient astronomy and the naked-eye planets". Eternal Gadgetry. MS. Retrieved January 6, 2018.
52. ^ Cotter, Garrett (2012). "High-Energy Astrophysics Lecture" (PDF). Astrophysics | University of Oxford Department of Physics.
53. ^ Berard (April 2009). "IRIG 106 Telemetry Standard Chapter 10" (PDF). U.S. Army White Sands Missile Range, New Mexico: Range Commanders Council. Archived (PDF) from the original on 2020-11-12. Retrieved 2010-11-10.
54. doi:10.1117/1.1426078
    .
55. ^ "Maximum password age". Microsoft TechNet. Retrieved 15 January 2014.
56. ISBN 978-0299225544
    .
57. ISBN 978-0299225544
    .
58. ISBN 978-0299225544
    .
59. ^ Clement of Alexandria (1885). "Book VI:IV". In Roberts, Alexander; James, Sir; Coxe, Arthur (eds.). The Stromata, or Miscellanies (With Active Table of Contents) (Kindle ed.). p. Kindle Location 11498.
60. ISBN 978-0299225544
    .
61. ISBN 978-0299225544
    .
62. ^ Ganzfried, R. Solomon (1902). קסת הסופר [Keset haSofer] (in Hebrew and English). Translated by Friendman, Jen (First ed.). Bardejov: דפוס יוסף מאיר בלייער. It is the custom to have no fewer than 48 lines, representing the journeys of Israel, and some say no fewer than 42, because of what God did in the Sinai wilderness at Kadesh. Also, we don't have more than 60 lines, representing the 60 myriads of Israel who received the Torah.
63. ^ Jacobs, Joseph; Eisenstein, Judah; Executive Committee of the Editorial Board; Blau, Ludwig (1906). "Scroll of the Law (Hebrew, "Sefer Torah")". Jewish Encyclopedia. Retrieved 12 February 2020. (At the present day the forty-two-lined column is the generally accepted style of the scroll, its length being about 24 inches.)
64. ^ Joel Primack; Nancy E. Abrams. "In A Beginning...Quantum Cosmology and Kabbalah" (PDF). Retrieved 2008-03-14.
65. ^ Niiya, Brian. Japanese American history: an A-to-Z reference from 1868 to the present. Facts on File, Inc., 1993, p. 352
66. ^ "Mathematical Fiction: Hitchhiker's Guide to the Galaxy (1979)". Retrieved 30 November 2016. See this website for possible explanations of this seeming error.
67. ^ "17 amazing Google Easter eggs". CBS News. November 11, 2011. Retrieved November 1, 2022.
68. ^ "Lewis Carroll and Douglas Adams – Word Ways – Find Articles". 29 June 2012. Archived from the original on 29 June 2012.
69. ^ The Mystery of Lewis Carroll, Jenny Woolf
70. ^ Carroll, Lewis. "The Hunting of the Snark".
71. ^ Carroll, Lewis. "The Hunting of the Snark".
72. ^ What Lewis Carroll Taught Us: Alice's creator knew all about role-playing. by Seth Lerer, March 4, 2010
73. ^ Walker, Carter (2016-07-15). "REVIEW: Music, not problems, is focus this year at Disco Biscuits' Camp Bisco at Pavilion at Montage". baltimoresun.com. Retrieved 2020-08-17.
74. ^ "Watson Jeopardy! computer: Ken Jennings describes what it's like to play against a machine". Slate. Retrieved 2 October 2015.
75. ISBN 978-0-307-49846-5
    .
76. ^ "The Laws of Cricket". Archived from the original on 29 August 2017. Retrieved 26 January 2017.
77. ^ Okrent, Daniel. Great Fortune: the Epic of the Rockefeller Centre. Viking Penguin, 2003, p. 147
78. ^ Okrent, Daniel. Great Fortune: the Epic of the Rockefeller Centre. Viking Penguin, 2003, p. 162
79. ^ Renfro, Kim (February 26, 2019). "Why the number 42 was hidden in plain sight throughout 'Spider-Man: Into the Spider-Verse'". Insider Inc. Retrieved November 29, 2019.
80. ^ "Tower 42 – City of London". cityoflondon.gov.uk. Retrieved 23 October 2018.
81. ^ "42: Neues KI-Start-up von Jajah-Gründer Daniel Mattes". Futurezone. 22 November 2015. Retrieved 2015-11-22.
82. ^ BigThink.com How many times must you fold a paper to reach the Moon?, January 8, 2024

External links

Wikiquote has quotations related to 42 (number).

Look up forty-two in Wiktionary, the free dictionary.

Media related to 42 (number) at Wikimedia Commons

• Grime, James; Gerardo Adesso; Phil Moriarty. "42 and Douglas Adams". Numberphile. Brady Haran. Archived from the original on 2018-10-13. Retrieved 2013-04-08.
• My latest favorite Number: 42, John C. Baez
• The number Forty-two in real life