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 A164573 Numbers n such that n and n+5 are prime powers. 6

%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, 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.]

%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^n-5),listput(v,2^n-5));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

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)