181 (number)

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← 180 181 182 →
Cardinal one hundred eighty-one
Ordinal 181st
(one hundred eighty-first)
Factorization prime
Prime 42nd
Divisors 1, 181
Greek numeral ΡΠΑ´
Roman numeral CLXXXI
Binary 101101012
Ternary 202013
Senary 5016
Octal 2658
Duodecimal 13112
Hexadecimal B516

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

Contents

In mathematics

181 is prime, and a palindromic, [1] 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 prime reciprocal magic square repeat 180 digits with a magic sum of 810; this value is one less than 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 ; [16] the next such full, prime reciprocal magic square is based on multiples of the reciprocal of 383 (also palindromic). [17] [lower-alpha 1]

181 is an undulating number in ternary and nonary numeral systems, while in decimal it is the 28th undulating prime. [18]

In other fields

181 is also:

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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.). "SequenceA002385(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.). "SequenceA007597(Strobogrammatic primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA134996(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.). "SequenceA109611(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.). "SequenceA006512(Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA034964(Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA024352(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. 1 2 Sloane, N. J. A. (ed.). "SequenceA001844(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. 1 2 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.). "SequenceA005891(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. 1 2 Sloane, N. J. A. (ed.). "SequenceA003154(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.). "SequenceA069131(Centered 18-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-26.
  13. ↑ Sloane, N. J. A. (ed.). "SequenceA000040(The prime numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02.
  14. ↑ Sloane, N. J. A. (ed.). "SequenceA001913(Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02.
  15. ↑ Andrews, William Symes (1917). Magic Squares and Cubes (PDF). Chicago, IL: Open Court Publishing Company. pp. 176, 177. ISBN   9780486206585. MR   0114763. OCLC   1136401. Zbl   1003.05500.
  16. ↑ Sloane, N. J. A. (ed.). "SequenceA006003(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.). "SequenceA072359(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.). "SequenceA032758(Undulating primes (digits alternate).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02.


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