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

1689, 1741, 3306, 3894, 4362, 4587, 4999, 5754, 6025, 6371, 6668, 7012, 7982, 9054, 9158, 9695, 9742, 9832, 10056, 10664, 11005, 12027, 12385, 13676, 13895, 14026, 14059, 16104, 16239, 16903, 17050, 17153, 18079, 18202, 18642, 20349, 21060

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = n-th integer i such that i^4 - 2 has no prime factor > i.

Example

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).

Prog

(PARI): 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++) a065903(40)

Crossrefs

Cf. A040028, A065902, A065904, A065905, A065906.

Sequence in context: A263061 A281062 A020241 * A204488 A062680 A251291

Adjacent sequences: A065900 A065901 A065902 * A065904 A065905 A065906

Keyword

nonn

Author

Klaus Brockhaus, Nov 28 2001

Status

approved