A051644 Primes of the form 6*p + 1 where p is also prime.

13, 19, 31, 43, 67, 79, 103, 139, 223, 283, 367, 439, 499, 607, 619, 643, 787, 823, 907, 1039, 1087, 1399, 1447, 1543, 1579, 1627, 1663, 1699, 1759, 1867, 1879, 1987, 2083, 2203, 2239, 2383, 2659, 2767, 2803, 3019, 3343, 3463, 3559, 3607, 3643, 3847, 3919

Offset

1,1

Comments

Analogous to A005385; can be called 6-safe primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Formula

a(n) = 6*A007693(n) + 1.

Example

103 is in the sequence because both 17 and 6*17 + 1 = 103 are primes.

Mathematica

Select[1 + 6Prime@Range[120], PrimeQ] (* Ray Chandler, Mar 14 2007 *)

Prog

(PARI) isok(k) = isprime(k) && k % 6 == 1 && isprime((k-1)/6); \\ Amiram Eldar, Feb 24 2025

Crossrefs

Cf. A005384, A005385, A002476, A007693, A016921, A024899, A091178.

Sequence in context: A069324 A040047 A163847 * A101408 A023252 A279426

Adjacent sequences: A051641 A051642 A051643 * A051645 A051646 A051647

Keyword

nonn,easy,changed

Author

Labos Elemer

Extensions

Edited, corrected and extended by Ray Chandler, Mar 14 2007

Status

approved