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 A164574 Numbers n such that n and n+6 are 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 (list; graph; refs; listen; history; text; internal format)
 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 Daniel Forgues, Table of n, a(n) for n = 1..2492 MATHEMATICA Join[{1}, Select[Range, 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 Cf. A023201, A000961. Cf. A006549 Numbers n such that n and n+1 are prime powers. Cf. A120431 Numbers n such that n and n+2 are prime powers. Cf. A164571 Numbers n such that n and n+3 are prime powers. Cf. A164572 Numbers n such that n and n+4 are prime powers. Cf. A164573 Numbers n such that n and n+5 are prime powers. Cf. A164574 Numbers n such that n and n+6 are prime powers. Sequence in context: A257688 A257689 A257691 * A079603 A095959 A028905 Adjacent sequences:  A164571 A164572 A164573 * A164575 A164576 A164577 KEYWORD nonn AUTHOR Daniel Forgues, Aug 16 2009 EXTENSIONS Edited by Daniel Forgues, Aug 17 2009 STATUS approved

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Last modified February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)