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

1,2

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)

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 *)

Prog

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

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).

Sequence in context: A257688 A257689 A257691 * A344023 A079603 A095959

Adjacent sequences: A164571 A164572 A164573 * A164575 A164576 A164577

Keyword

nonn

Author

Daniel Forgues, Aug 16 2009

Extensions

Edited by Daniel Forgues, Aug 17 2009

Status

approved