A154773 Numbers n such that 252n^2 is the average of a twin prime pair.

3, 5, 11, 14, 18, 20, 26, 27, 28, 29, 31, 38, 42, 52, 58, 64, 73, 82, 85, 90, 110, 125, 138, 156, 167, 180, 212, 234, 248, 297, 299, 303, 305, 308, 312, 314, 317, 319, 334, 336, 348, 361, 365, 371, 372, 377, 379, 414, 451, 465, 478, 499, 508, 509, 535, 554, 564

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 A154673 as 252 a(n)^2. Indeed, if N/7 is a square, then N=7m^2 and this can't be the average of a twin prime pair unless m=6a.

Links

• Zak Seidov, "A154676", Jan 15 2009

Crossrefs

Cf. A037073, A154331, A154772.

Programs

Mathematica

Select[Range[600],And@@PrimeQ[252#^2+{1,-1}]&] (* Harvey P. Dale, Dec 13 2012 *)

PARI

for(i=1,999, isprime(252*i^2+1) & isprime(252*i^2-1) & print1(i","))

Formula

a(n) = sqrt(A154673(n)/252).