181 (number)

Last updated
← 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:

See also

Related Research Articles

10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.

27 is the natural number following 26 and preceding 28.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen.

55 (fifty-five) is the natural number following 54 and preceding 56.

101 is the natural number following 100 and preceding 102.

109 is the natural number following 108 and preceding 110.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

360 is the natural number following 359 and preceding 361.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

800 is the natural number following 799 and preceding 801.

2000 is a natural number following 1999 and preceding 2001.

151 is a natural number. It follows 150 and precedes 152.

138 is the natural number following 137 and preceding 139.

313 is the natural number following 312 and preceding 314.

744 is the natural number following 743 and preceding 745.

20,000 is the natural number that comes after 19,999 and before 20,001.

60,000 (sixty thousand) is the natural number that comes after 59,999 and before 60,001. It is a round number. It is the value of (F25).

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.


This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.