A116958 Numbers k such that 2*k + 5 and 2*k + 7 are twin primes.

0, 3, 6, 12, 18, 27, 33, 48, 51, 66, 72, 87, 93, 96, 111, 117, 132, 138, 153, 171, 207, 213, 228, 258, 282, 297, 306, 318, 327, 402, 408, 411, 426, 438, 507, 513, 522, 528, 543, 573, 612, 636, 642, 648, 657, 711, 723, 738, 741, 801, 807, 831, 846, 858, 891, 933

Offset

1,2

Comments

All k's are multiples of 3 because all twin primes except (3,5) are of the form (6*k-1, 6*k+1). - Jonathan Vos Post, Mar 31 2006

Links

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

Eric Weisstein's World of Mathematics, Twin Primes.

Formula

a(n) = 3 * (A002822(n)-1). [Corrected by Georg Fischer, Oct 19 2023]

Mathematica

Reap[Do[If[PrimeQ[2n+5]&&PrimeQ[2n+7], Sow[n]], {n, 0, 1000}]][[2, 1]]
Select[Range[0, 1000], AllTrue[2#+{5, 7}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 25 2019 *)

Crossrefs

Cf. A002822, A014574.

Sequence in context: A024513 A181026 A180005 * A242477 A006156 A171370

Adjacent sequences: A116955 A116956 A116957 * A116959 A116960 A116961

Keyword

nonn

Author

Zak Seidov, Mar 30 2006

Status

approved