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 A154775 Numbers k such that 13*(6*k)^2 is the average of a twin prime pair. 2
 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 (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 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: A126666 A036983 A303006 * A210418 A167454 A056683 Adjacent sequences:  A154772 A154773 A154774 * A154776 A154777 A154778 KEYWORD nonn AUTHOR M. F. Hasler, Jan 15 2009 STATUS approved

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Last modified June 2 18:09 EDT 2020. Contains 334787 sequences. (Running on oeis4.)