A156655 Primes of the form 1000*k + 1.

3001, 4001, 7001, 9001, 13001, 16001, 19001, 21001, 24001, 28001, 51001, 54001, 55001, 61001, 69001, 70001, 76001, 81001, 88001, 90001, 93001, 96001, 97001, 102001, 103001, 109001, 114001, 115001, 121001, 123001, 124001, 126001, 129001

Offset

1,1

Comments

Let d be any divisors of 1000, then d and -d are quadratic residues modulo these primes. All terms are of the form x^2 - d*y^2 for d = -40, -25, -10, -8, -5, -4, -2, -1, 2, 5, 8, 10. Conjecture: they are also of the form x^2 - d*y^2 for d = 20, 40, 50, 200. - Jianing Song, Aug 29 2018

Links

Table of n, a(n) for n=1..33.

Prog

(PARI) for(k=0, 130, if(isprime(1000*k+1), print1(1000*k+1, ", "))) \\ Jianing Song, Aug 29 2018

Crossrefs

Cf. A064962.

Sequence in context: A229782 A269885 A269764 * A128935 A145304 A094336

Adjacent sequences: A156652 A156653 A156654 * A156656 A156657 A156658

Keyword

nonn

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 12 2009

Extensions

More terms from R. J. Mathar, Feb 19 2009

Status

approved