cp's OEIS Frontend

A065903 Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2.

%I A065903 #8 Feb 24 2025 10:48:35
%S A065903 1689,1741,3306,3894,4362,4587,4999,5754,6025,6371,6668,7012,7982,
%T A065903 9054,9158,9695,9742,9832,10056,10664,11005,12027,12385,13676,13895,
%U A065903 14026,14059,16104,16239,16903,17050,17153,18079,18202,18642,20349,21060
%N A065903 Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2.
%C A065903 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 one resp. two resp. three prime factors > i; cf. A065904 resp. A065905 resp. A065906.
%F A065903 a(n) = n-th integer i such that i^4 - 2 has no prime factor > i.
%e A065903 a(2) = 1741, since 1741 is (after 1689) the second integer i for which there are no primes p > i such that i is a solution mod p of x^4 = 2, or equivalently, 1741^4 - 2 = 9187452028559 = 7*7*79*887*1609*1663 has no prime factor > 1741. (cf. A065902).
%o A065903 (PARI)
%o A065903 a065903(m) = local(c,n,f,a); c = 0; n = 2; while(c<m,f = factor(n^4-2); a = matsize(f)[1]; if(f[a,1]<= n,print1(n,","); c++); n++)
%o A065903 a065903(40)
%Y A065903 Cf. A040028, A065902, A065904, A065905, A065906.
%K A065903 nonn
%O A065903 1,1
%A A065903 _Klaus Brockhaus_, Nov 28 2001