

A154772


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


4



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
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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^21) & 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



