%I
%S 2,3,4,8,11,27,32,59,251,1019,2048,4091,262139,1048571,67108859,
%T 4294967291,68719476731,140737488355328,9007199254740992,
%U 72057594037927931,73786976294838206459,332306998946228968225951765070086139
%N Numbers n such that n and n+5 are prime powers.
%C Numbers n such that n + (0, 5) is a prime power pair.
%C n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.
%C n + (0, 2m1), m >= 1, being a nonadmissible pattern for prime pairs, since (0, 2m1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a  2m1, 2^a) or (2^a, 2^a + 2m1), a >= 0.]
%C Numbers n such that n and n+5 are primes would give only 2, for the prime pair (2, 7).
%C 10^18 < a(21) <= 73786976294838206459.  _Donovan Johnson_, Aug 17 2009
%H Charles R Greathouse IV, <a href="/A164573/b164573.txt">Table of n, a(n) for n = 1..37</a>
%o (PARI) is(n)=if(n<5,return(n>1)); isprimepower(n) && isprimepower(n+5) \\ _Charles R Greathouse IV_, Apr 24 2015
%o (PARI) v=List();for(n=0,1e3,if(isprimepower(2^n5),listput(v,2^n5));if(isprimepower(2^n+5),listput(v,2^n))); Set(v) \\ _Charles R Greathouse IV_, Apr 24 2015
%Y Cf. A006549 Numbers n such that n and n+1 are prime powers.
%Y Cf. A120431 Numbers n such that n and n+2 are prime powers.
%Y Cf. A164571 Numbers n such that n and n+3 are prime powers.
%Y Cf. A164572 Numbers n such that n and n+4 are prime powers.
%Y Cf. A164573 Numbers n such that n and n+5 are prime powers.
%Y Cf. A164574 Numbers n such that n and n+6 are prime powers.
%K nonn
%O 1,1
%A _Daniel Forgues_, Aug 16 2009
%E Edited by _Daniel Forgues_, Aug 17 2009
%E a(13)a(20) from _Donovan Johnson_, Aug 17 2009
%E a(21)a(22) from _Charles R Greathouse IV_, Apr 24 2015
