A098828 Primes of the form 2*n^2 + 2*n - 1.

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

Author

Giovanni Teofilatto, Oct 09 2004

Keywords

• nonn

Comments

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

Crossrefs

Cf. A109358, A109367, A153238

Programs

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) ];

Mathematica

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

PARI

list(lim)=my(v=List()); for(n=1,oo, my(t=2*n*(n+1)-1); if(t>lim, return(Vec(v))); if(isprime(t), listput(v,t))) \\ Charles R Greathouse IV, Feb 26 2025

Formula

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

Extensions

Corrected by Ray Chandler, Oct 26 2004

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

Name edited by Charles R Greathouse IV, Feb 26 2025