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

1,2

Links

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

C. K. Caldwell, Twin primes

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000290, A001359, A006512, A173165.

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

Sequence in context: A053013 A070044 A129850 * A358535 A329407 A329408

Adjacent sequences: A037070 A037071 A037072 * A037074 A037075 A037076

Keyword

nonn

Author

G. L. Honaker, Jr.

Extensions

More terms from Jud McCranie, Dec 30 2000

Status

approved