login
A164574
Numbers k such that k and k+6 are both prime powers.
6
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
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: A257689 A257691 A372059 * A344023 A079603 A095959
KEYWORD
nonn
AUTHOR
Daniel Forgues, Aug 16 2009
EXTENSIONS
Edited by Daniel Forgues, Aug 17 2009
STATUS
approved