A154772 Numbers m such that 180 m^2 is the average of a twin prime pair.

1, 3, 7, 14, 22, 29, 41, 46, 62, 64, 67, 88, 167, 179, 207, 231, 239, 249, 263, 266, 286, 290, 309, 315, 322, 323, 326, 344, 350, 353, 354, 372, 392, 421, 444, 454, 458, 496, 505, 553, 560, 561, 571, 585, 613, 636, 647, 661, 669, 682, 745, 788, 790, 791, 815

Offset

1,2

Comments

Inspired by Z. Seidov's post to the SeqFan list, cf. link. This yields A154672 as 180 a(n)^2. Indeed, if N is such that N/5 is a square, then M=5m^2 and this can't by the average of a twin prime pair unless m=6a.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Zak Seidov, "A154676", Jan 15 2009

Formula

a(n) = sqrt(A154672(n)/180)

Mathematica

Select[Range[10^3], And @@ PrimeQ[180#^2 + {-1, 1}] &] (* Amiram Eldar, Dec 25 2019 *)

Prog

(PARI) for(i=1, 999, isprime(180*i^2+1) & isprime(180*i^2-1) & print1(i", "))

Crossrefs

Cf. A014574, A037073, A154331, A154672.

Sequence in context: A258434 A249341 A310278 * A156859 A173209 A331240

Adjacent sequences: A154769 A154770 A154771 * A154773 A154774 A154775

Keyword

nonn

Author

M. F. Hasler, Jan 15 2009

Status

approved