A154775 Numbers k such that 13*(6*k)^2 is the average of a twin prime pair.

2, 4, 5, 42, 46, 49, 59, 82, 84, 100, 119, 128, 137, 182, 185, 187, 192, 233, 264, 301, 303, 340, 376, 390, 395, 422, 438, 446, 471, 472, 494, 518, 527, 570, 598, 609, 611, 633, 667, 688, 714, 716, 726, 728, 733, 744, 831, 837, 865, 875, 896, 926, 940, 948

Offset

1,1

Comments

Inspired by Zak Seidov's post to the SeqFan list, cf. link: This yields A154675 as 468 a(n)^2. Indeed, if N/13 is a square, then N=13 k^2 and this can't be the average of a twin prime pair unless k=6m.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Zak Seidov, "A154676", Jan 15 2009

Formula

a(n) = sqrt(A154675(n)/468).

Mathematica

okQ[n_]:=Module[{av=468n^2}, PrimeQ[av-1]&&PrimeQ[av+1]]; Select[Range[1000], okQ] (* Harvey P. Dale, Jan 21 2011 *)

Prog

(PARI) for(i=1, 999, isprime(468*i^2+1) & isprime(468*i^2-1) & print1(i", "))

Crossrefs

Cf. A014574, A037073, A154331, A154772, A154773, A154774, A154675.

Sequence in context: A036983 A370438 A303006 * A210418 A167454 A056683

Adjacent sequences: A154772 A154773 A154774 * A154776 A154777 A154778

Keyword

nonn

Author

M. F. Hasler, Jan 15 2009

Status

approved