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 A065906 #6 Feb 10 2025 15:04:21 %S A065906 15,48,55,197,206,221,235,283,297,408,444,472,489,577,578,623,641,677, %T A065906 701,703,763,854,930,1049,1081,1134,1140,1159,1160,1201,1253,1303, %U A065906 1311,1328,1374,1385,1415,1458,1459,1495,1501,1517,1557,1585,1714,1723,1726 %N A065906 Integers i > 1 for which there are three primes p such that i is a solution mod p of x^4 = 2. %C A065906 Solutions mod p are represented by integers from 0 to p-1. The following equivalences holds for i > 1: There is a prime p such that i is a solution mod p of x^4 = 2 iff i^4 - 2 has a prime factor > i; i is a solution mod p of x^4 = 2 iff p is a prime factor of i^4 - 2 and p > i. i^4 - 2 has at most three prime factors > i. For i such that i^4 - 2 has no resp. one resp. two prime factors > i cf. A065903 resp. A065904 resp. A065905. %F A065906 a(n) = n-th integer i such that i^4 - 2 has three prime factors > i. %e A065906 a(3) = 55, since 55 is (after 15 and 48) the third integer i for which there are three primes p > i (viz. 73, 103 and 1217) such that i is a solution mod p of x^4 = 2, or equivalently, 55^4 - 2 = 9150623 = 73*103*1217 has three prime factors > 4. (cf. A065902). %o A065906 (PARI) %o A065906 a065906(m) = local(c,n,f,a,s,j); c = 0; n = 2; while(c<m,f = factor(n^4-2); a = matsize(f)[1]; s = []; for(j = 1,a, if(f[j,1]>n,s = concat(s,f[j,1]))); if(matsize(s)[2] == 3,print1(n,","); c++); n++) %o A065906 a065906(50) %Y A065906 Cf. A040028, A065902, A065903, A065904, A065905. %K A065906 nonn %O A065906 1,1 %A A065906 _Klaus Brockhaus_, Nov 28 2001