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

Author

M. F. Hasler, Jan 15 2009

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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