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
KEYWORD
nonn
AUTHOR
Daniel Forgues, Aug 16 2009
EXTENSIONS
Edited by Daniel Forgues, Aug 17 2009
STATUS
approved