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

1,1

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

Table of n, a(n) for n=1..57.

Zak Seidov, "A154676", Jan 15 2009

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A037073, A154331, A154772.

Sequence in context: A162875 A166564 A058595 * A176658 A086284 A136500

Adjacent sequences: A154770 A154771 A154772 * A154774 A154775 A154776

Keyword

nonn

Author

M. F. Hasler, Jan 15 2009

Status

approved