181 (number)

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← 180 181 182 →
Cardinalone hundred eighty-one
Ordinal181st
(one hundred eighty-first)
Factorizationprime
Prime42nd
Divisors1, 181
Greek numeralΡΠΑ´
Roman numeralCLXXXI
Binary101101012
Ternary202013
Senary5016
Octal2658
Duodecimal13112
HexadecimalB516

181 (one hundred [and] eighty-one) is the natural number following 180 and preceding 182.

In mathematics

181 is

strobogrammatic,[2] and dihedral number[3] in decimal. 181 is a Chen prime.[4]

181 is a twin prime with 179,[5] equal to the sum of five consecutive prime numbers:[6] 29 + 31 + 37 + 41 + 43.

181 is the difference of

two consecutive square numbers 912 – 902,[7] as well as the sum of two consecutive squares: 92 + 102.[8]

As a centered polygonal number,[9] 181 is:

181 is also a centered (hexagram) star number,[11] as in the game of Chinese checkers.

Specifically, 181 is the 42nd prime number[13] and 16th full reptend prime in decimal,[14] where multiples of its reciprocal inside a

magic sum
of
811, the 141st prime number and 49th full reptend prime (or equivalently long prime) in decimal whose reciprocal repeats
810 digits. While the first full non-normal prime reciprocal magic square is based on with a magic constant of 81 from a square,[15] a normal magic square has a magic constant ;
383 (also palindromic).[17][a]

181 is an

nonary numeral systems, while in decimal it is the 28th undulating prime.[18]

In other fields

181 is also:

See also

References

  1. ^ Where the full reptend index of 181 is 16 = 42, the such index of 811 is 49 = 72. Note, also, that 282 is 141 × 2.
  1. ^ Sloane, N. J. A. (ed.). "Sequence A002385 (Palindromic primes: prime numbers whose decimal expansion is a palindrome.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A007597 (Strobogrammatic primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A134996 (Dihedral calculator primes: p, p upside down, p in a mirror, p upside-down-and-in-a-mirror are all primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A024352 (Numbers which are the difference of two positive squares, c^2 - b^2 with 1 less than or equal to b less than c.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  8. ^ a b Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers: a(n) equal to 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z is Y+1) ordered by increasing Z; then sequence gives Z values.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
  9. ^ a b Sloane, N. J. A. (ed.). "Centered polygonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
  11. ^ a b Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A069131 (Centered 18-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  14. ^ Sloane, N. J. A. (ed.). "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  15. Zbl 1003.05500
    .
  16. ^ Sloane, N. J. A. (ed.). "Sequence A006003 (a(n) equal to n*(n^2 + 1)/2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A072359 (Primes p such that the p-1 digits of the decimal expansion of k/p (for k equal to 1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-04.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A032758 (Undulating primes (digits alternate).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.

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