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A253644
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Numbers n such that n^k is zeroless for k=0,...,5.
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5
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1, 2, 3, 5, 6, 13, 14, 17, 23, 24, 26, 31, 58, 62, 66, 68, 72, 76, 88, 96, 137, 168, 188, 233, 244, 262, 264, 296, 337, 376, 382, 383, 483, 488, 511, 514, 518, 519, 582, 628, 719, 736, 786, 816, 822, 928, 938, 971, 978, 1122, 1178, 1291, 1331, 1392, 1413, 1414, 1663, 1777
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OFFSET
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1,2
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COMMENTS
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A subsequence of A252484 (analog for k <= 4) which contains A253647 (analog including k = 6) as a subsequence. Primes in this sequence are listed in A253645.
Conjectured to be finite.
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LINKS
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MAPLE
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filter:= proc(x)
local k;
for k from 1 to 5 do
if has(convert(x^k, base, 10), 0) then return false fi
od:
true
end proc:
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MATHEMATICA
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Select[Range[2000], Count[Flatten[IntegerDigits/@(#^Range[5])], 0]==0&] (* Harvey P. Dale, Jun 10 2017 *)
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PROG
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(PARI) is_A253644(n, K=5)=!forstep(k=K, 1, -1, vecmin(digits(n^k))||return)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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