A037073 Numbers k such that (6*k)^2 is the sum of a twin prime pair.

1, 2, 7, 8, 12, 14, 15, 29, 34, 44, 51, 62, 68, 76, 79, 91, 99, 100, 107, 125, 142, 147, 156, 162, 163, 173, 190, 202, 212, 231, 245, 252, 253, 264, 295, 306, 317, 330, 331, 355, 366, 376, 377, 386, 397, 442, 448, 453, 462, 469, 481, 491, 498, 502, 516, 547

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn

Examples

			E.g. n=44 -> (6*44)^2 = 69696 = 34847 + 34849 (twin prime pair).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• C. K. Caldwell, Twin primes

Crossrefs

Cf. A000290, A001359, A006512, A173165.

A152786 = 6*A037073. - Zak Seidov, Aug 20 2010

Programs

Maple

isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):
select(isa, [$4..1000000]): map(n -> sqrt(2*n+2)/6, %); # Peter Luschny, Jan 05 2020

Mathematica

Select[Sqrt[Plus@@@Select[Partition[Prime[Range[4*10^5]],2,1],Differences[#]=={2} &]/36],IntegerQ] (* Jayanta Basu, May 26 2013 *)

PARI

is(n)=isprime(18*n^2-1)&&isprime(18*n^2+1) \\ M. F. Hasler, Oct 30 2023

Formula

a(n) = A173165(n)/3. - M. F. Hasler, Oct 30 2023

Extensions

More terms from Jud McCranie, Dec 30 2000