181 (number)

181 prime 42nd 1, 181 181 (one hundred [and] eighty-one) is the natural number following 180 and preceding 182. In mathematics 181 is prime, and a palindromic,A002385 Palindromic primes: prime numbers whose decimal expansion is a palindrome. 2023-11-02 strobogrammatic,A007597 Strobogrammatic primes. 2023-11-02 and dihedral numberA134996 Dihedral calculator primes: p, p upside down, p in a mirror, p upside-down-and-in-a-mirror are all primes. 2023-11-02 in decimal. 181 is a Chen prime.A109611 Chen primes: primes p such that p + 2 is either a prime or a semiprime. 2016-05-26 181 is a twin prime with 179,A006512 Greater of twin primes. 2023-11-02 equal to the sum of five consecutive prime numbers:A034964 Sums of five consecutive primes. 2023-11-02 29 + 31 + 37 + 41 + 43. 181 is the difference of two consecutive square numbers 912 – 902,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. 2023-11-02 as well as the sum of two consecutive squares: 92 + 102.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. 2016-05-26 As a centered polygonal number,Sloane, N. J. A. Neil Sloane Centered polygonal numbers The On-Line Encyclopedia of Integer Sequences https://oeis.org/wiki/Centered_polygonal_numbers OEIS Foundation 2023-11-02 181 is: a centered square number, a centered pentagonal number,A005891 Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net. 2016-05-26 a centered dodecagonal number,A003154 Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1. 2016-05-26 a centered 18-gonal number,A069131 Centered 18-gonal numbers. 2016-05-26 and a centered 30-gonal number. 181 is also a centered (hexagram) star number, as in the game of Chinese checkers. Specifically, 181 is the 42nd prime numberA000040 The prime numbers 2023-11-02 and 16th full reptend prime in decimal,A001913 Full reptend primes: primes with primitive root 10. 2023-11-02 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,Andrews William Symes Magic Squares and Cubes http://djm.cc/library/Magic_Squares_Cubes_Andrews_edited.pdf 2nd Open Court Publishing Company Chicago, IL 1917 176, 177 1136401 1003.05500 0114763 a normal magic square has a magic constant ;A006003 a(n) equal to n*(n^2 + 1)/2. 2023-11-02 the next such full, prime reciprocal magic square is based on multiples of the reciprocal of 383 (also palindromic).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. 2023-09-04 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. 181 is an undulating number in ternary and nonary numeral systems, while in decimal it is the 28th undulating prime.A032758 Undulating primes (digits alternate). 2023-11-02 References External links Prime curiosities: 181 Number Facts and Trivia: 181 Number Gossip: 181 1 Category:Integers Category: Prime numbers