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

Author

M. F. Hasler, Jan 15 2009

Keywords

• nonn

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

Crossrefs

Cf. A014574, A037073, A154331, A154672.

Programs

Mathematica

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

PARI

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

Formula

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