This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059940 #4 Mar 30 2012 17:27:32 %S A059940 3,5,31,41,107,11,17,727,499,443,863,439,457,3373,23,1637,53,6857,31, %T A059940 47,5323,811,6911,919,29,19681,439,739,13499,29789,43,7187,43,461, %U A059940 23327,50651,59,2579,2909,22973,2179,15901,14197,293,1187,34607,11059 %N A059940 Smallest prime p such that x = n is a solution mod p of x^3 = 2, or 0 if no such prime exists. %C A059940 Solutions mod p are represented by integers from 0 to p-1. The following equivalences hold for n > 1: There is a prime p such that n is a solution mod p of x^3 = 2 iff n^3-2 has a prime factor > n; n is a solution mod p of x^3 = 2 iff p is a prime factor of n^3-2 and p > n. %C A059940 n^3-2 has at most two prime factors > n, consequently these factors are the only primes p such that n is a solution mod p of x^3 = 2. For n such that n^3-2 has no prime factor > n (the zeros in the sequence; they occur beyond the last entry shown in the database) see A060591. For n such that n^3-2 has two prime factors > n, cf. A060914. %F A059940 If n^3-2 has prime factors > n, then a(n) = least of these prime factors, else a(n) = 0. %e A059940 a(2) = 3, since 2 is a solution mod 3 of x^3 = 2 and 2 is not a solution mod p of x^3 = 2 for prime p = 2. Although 2^3 = 2 mod 2, prime 2 is excluded because 0 < 2 and 2 = 0 mod 2. a(5) = 41, since 5 is a solution mod 41 of x^3 = 2 and 5 is not a solution mod p of x^3 = 2 for primes p < 41. Although 5^3 = 2 mod 3, prime 3 is excluded because 3 < 5 and 5 = 2 mod 3. %Y A059940 Cf. A040028, A060121, A060122, A060123, A060124, A060591, A060914. %K A059940 nonn %O A059940 2,1 %A A059940 _Klaus Brockhaus_, Mar 02 2001