A164574 Numbers k such that k and k+6 are both prime powers.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 31, 37, 41, 43, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 121, 125, 131, 151, 157, 163, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 283, 307, 311, 331, 337, 343, 347, 353, 361, 367, 373, 383, 433, 443, 457

Offset: 1

Author

Daniel Forgues, Aug 16 2009

Keywords

• nonn

Comments

Numbers n such that n + (0, 6) is a prime power pair.

n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.

n + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, since (0, 2m-1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.]

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2492 from Daniel Forgues)

Crossrefs

Cf. A023201, A000961.

k and (x) are prime powers: A006549 (k+1) A120431 (k+2), A164571 (k+3), A164572 (k+4), A164573 (k+5), this sequence (k+6).

Programs

Mathematica

Join[{1},Select[Range[500],AllTrue[{#,#+6},PrimePowerQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 30 2018 *)

PARI

is(n)=if(n<4,return(n>0)); isprimepower(n) && isprimepower(n+6) \\ Charles R Greathouse IV, Apr 24 2015

Extensions

Edited by Daniel Forgues, Aug 17 2009