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A154773 Numbers n such that 252n^2 is the average of a twin prime pair. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)