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 A065912 #8 Mar 18 2025 16:06:37 %S A065912 55,84,86,205,222,235,206,305,325,489,556,494,830,928,964,972,1046, %T A065912 976,721,940,1162,1132,1065,871,1469,1289,1328,1477,1594,1253,1760, %U A065912 1604,1782,1877,1883,1442,2002,2114,2144,1709,2112,1909,2277,2343,2492,2735 %N A065912 Fourth solution mod p of x^4 = 2 for primes p such that more than two solution exists. %C A065912 Conjecture: no integer occurs more than three time in this sequence. Confirmed for the first 1182 terms of A014754 (primes < 100000). In this section, there are no integers which do occur thrice. Moreover, no integer is first, second, third or fourth solution for more than three primes. Confirmed for the first 2399 terms of A007522 and the first 1182 terms of A014754 (primes < 100000). %F A065912 a(n) = fourth solution mod p of x^4 = 2, where p is the n-th prime such that x^4 = 2 has more than two solutions mod p, i.e. p is the n-th term of A014754. %e A065912 a(3) = 86, since 113 is the third term of A014754, 27, 47, 66 and 86 are the solutions mod 113 of x^4 = 2 and 86 is the fourth one. %o A065912 (PARI) %o A065912 a065912(m) = local(s); forprime(p = 2,m,s = []; for(x = 0,p-1, if(x^4%p == 2%p,s = concat(s,[x]))); if(matsize(s)[2]>3,print1(s[4],","))) %o A065912 a065912(3000) %Y A065912 Cf. A040098, A007522, A014754, A065909, A065910, A065911. %K A065912 nonn %O A065912 1,1 %A A065912 _Klaus Brockhaus_, Nov 29 2001