A098828 Primes of the form 3x^2 - y^2, where x and y are two consecutive numbers.

3, 11, 23, 59, 83, 179, 263, 311, 419, 479, 683, 839, 1103, 1511, 2111, 2243, 2663, 2963, 3119, 4139, 4703, 5099, 5303, 5939, 7079, 10223, 11399, 12011, 12323, 12959, 17483, 19403, 21011, 21839, 22259, 24419, 25763, 27143, 27611, 28559, 30011

Offset

1,1

Comments

Equivalently primes of the form 2n^2 - 2n - 1. a(n)==3 (mod 4).

Equivalently primes p such that 2p+3 is square.

Also 3 followed by primes p of the form 2*n^2+6*n+3 = 2*(n+2)^2-2*(n+2)-1 (see the first comment) such that 2^(p-1)+3 is not prime. - Vincenzo Librandi, Jan 03 2009; M. F. Hasler, Jan 07 2009; R. J. Mathar, Jan 14 2009; Bruno Berselli, Sep 23 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = (A109367(n) - 3)/2.

Mathematica

Select[Table[Prime[n], {n, 3500}], IntegerQ[(2# + 3)^(1/2)] &] (* Ray Chandler, Oct 26 2004 *)

Prog

(Magma) [3] cat [ p: p in PrimesUpTo(30100) | exists(t){ n: n in [1..Isqrt(p div 2)] | 2*n^2+6*n+3 eq p } and not IsPrime(2^(p-1)+3) ];

Crossrefs

Cf. A109358, A109367.

Cf. A153238

Sequence in context: A289888 A145477 A243887 * A165635 A337476 A301876

Adjacent sequences: A098825 A098826 A098827 * A098829 A098830 A098831

Keyword

nonn

Author

Giovanni Teofilatto, Oct 09 2004

Extensions

Corrected by Ray Chandler, Oct 26 2004

Edited by N. J. A. Sloane, Jan 25 2009

Status

approved