A007693 - OEIS

A007693

Primes p such that 6*p + 1 is also prime.
(Formerly M0656)

2, 3, 5, 7, 11, 13, 17, 23, 37, 47, 61, 73, 83, 101, 103, 107, 131, 137, 151, 173, 181, 233, 241, 257, 263, 271, 277, 283, 293, 311, 313, 331, 347, 367, 373, 397, 443, 461, 467, 503, 557, 577, 593, 601, 607, 641, 653, 661, 683, 727, 751, 761, 773, 787, 797, 853

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

Joe Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 83.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Andrew Granville, Sophie Germain's theorem for prime pairs p, 6p+1, J. Number Theory 27 (1987), no. 1, 63-72.

FORMULA

a(n) = (A051644(n)-1)/6.

MATHEMATICA

Select[Prime@Range[150], PrimeQ[6# + 1] &] (* Ray Chandler, Mar 14 2007 *)

PROG

(Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(6*n+1)]; // Vincenzo Librandi, Nov 18 2010

(PARI) isok(k) = isprime(k) && isprime(6*k+1); \\ Amiram Eldar, Feb 24 2025

CROSSREFS

Cf. A002476, A016921, A024899, A051644, A091178, A023256 (subset: 6*(6p+1)+1 also prime).

Prime terms of A024899.

Sequence in context: A268812 A283562 A152245 * A174048 A249644 A103144

Adjacent sequences: A007690 A007691 A007692 * A007694 A007695 A007696

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and Robert G. Wilson v

EXTENSIONS

Extended by Ray Chandler, Mar 14 2007

STATUS

approved