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 A164574 Numbers n such that n and n+6 are prime powers. 6

%I

%S 1,2,3,5,7,11,13,17,19,23,25,31,37,41,43,47,53,61,67,73,83,97,101,103,

%T 107,121,125,131,151,157,163,167,173,191,193,223,227,233,251,257,263,

%U 271,277,283,307,311,331,337,343,347,353,361,367,373,383,433,443,457

%N Numbers n such that n and n+6 are prime powers.

%C Numbers n such that n + (0, 6) 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.]

%H Daniel Forgues, <a href="/A164574/b164574.txt">Table of n, a(n) for n = 1..2492</a>

%t Join[{1},Select[Range[500],AllTrue[{#,#+6},PrimePowerQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 30 2018 *)

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

%Y Cf. A023201, A000961.

%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 1,2

%A _Daniel Forgues_, Aug 16 2009

%E Edited by _Daniel Forgues_, Aug 17 2009

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Last modified April 3 13:53 EDT 2020. Contains 333197 sequences. (Running on oeis4.)