A154774 Numbers n such that 9900n^2 is the average of a twin prime pair.

10, 14, 15, 25, 60, 74, 76, 87, 127, 129, 130, 140, 171, 196, 207, 224, 259, 263, 302, 314, 315, 319, 333, 337, 377, 389, 451, 454, 470, 491, 508, 518, 549, 568, 574, 589, 592, 624, 629, 636, 690, 696, 729, 748, 753, 769, 770, 771, 781, 791, 802, 833, 844

Offset

1,1

Comments

Inspired by Zak Seidov's post to the SeqFan list, cf. link: This yields A154674 as 9900 a(n)^2. Indeed, if N/11 is a square, then N=11 m^2 and this can't be the average of a twin prime pair unless m=30a (considering N+1 mod 2,3,5 and N-1 mod 5).

Links

Table of n, a(n) for n=1..53.

Zak Seidov, "A154676", Jan 15 2009

Formula

a(n) = sqrt(A154674(n)/9900).

Mathematica

Select[Range[1000], AllTrue[9900#^2+{1, -1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 19 2019 *)

Prog

(PARI) for(i=1, 999, isprime(9900*i^2+1) & isprime(9900*i^2-1) & print1(i", "))

Crossrefs

Cf. A037073, A154331, A154772-A154773.

Sequence in context: A271568 A229271 A088711 * A162708 A330210 A067188

Adjacent sequences: A154771 A154772 A154773 * A154775 A154776 A154777

Keyword

nonn

Author

M. F. Hasler, Jan 15 2009

Status

approved