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A065801
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Least k such that n^k > 2^n.
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1
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3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14
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OFFSET
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2,1
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LINKS
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EXAMPLE
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a(4) = 3 because if k = 2, 4^2 <= 2^4 but when k reaches 3, 4^3 > 2^4.
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MATHEMATICA
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a[n_] := (k = 1; While[n^k <= 2^n, k++ ]; Return[k]); Table[ a[n], {n, 2, 70} ]
lk[n_]:=Module[{k=Ceiling[Log[n, 2^n]], nt=2^n}, While[n^k<=nt, k++]; k]; Array[ lk, 90, 2] (* Harvey P. Dale, Mar 15 2018 *)
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PROG
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(PARI) { for (n=2, 1000, k=1; p=2^n; while (n^k <= p, k++); write("b065801.txt", n, " ", k) ) } \\ Harry J. Smith, Oct 31 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Offset changed from 1 to 2 and Definition corrected by Harry J. Smith, Oct 31 2009
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STATUS
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approved
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