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A329364
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Numbers k such that k, k+2, k+4 are prime powers.
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0
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1, 3, 5, 7, 9, 23, 25, 27, 79, 239, 59049, 450283905890997359, 36472996377170786399
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OFFSET
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1,2
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COMMENTS
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a(14) > 10^3000, if it exists. Note that one among k, k+2, k+4 is always divisible by 3, so it must be a power of 3. - Giovanni Resta, Nov 12 2019
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LINKS
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EXAMPLE
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7 is a term since 7, 9, and 11 are all prime powers.
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MATHEMATICA
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pp[w_] := w == 1 || And @@ PrimePowerQ[w + {0, 2, 4}]; Reap[ Do[ If[pp[n - k], Sow[n-k]], {n, 3^Range[100]}, {k, {4, 2, 0}}]][[2, 1]] (* Giovanni Resta, Nov 12 2019 *)
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PROG
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(PARI) isok(k) = (k==1) || (isprimepower(k) && isprimepower(k+2) && isprimepower(k+4)); \\ Michel Marcus, Nov 12 2019
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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