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A086824
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Least positive k such that k! >= n^k.
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2
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1, 1, 4, 7, 9, 12, 14, 17, 20, 22, 25, 28, 30, 33, 36, 38, 41, 44, 47, 49, 52, 55, 57, 60, 63, 65, 68, 71, 73, 76, 79, 82, 84, 87, 90, 92, 95, 98, 101, 103, 106, 109, 111, 114, 117, 119, 122, 125, 128, 130, 133, 136, 138, 141, 144, 147, 149, 152, 155, 157, 160, 163, 166
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OFFSET
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0,3
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COMMENTS
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Suggested by Richard-Andre Jeannin (andre-jeannin.richard(AT)wanadoo.fr).
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LINKS
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FORMULA
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a(n) = e*n + O(log(n)); a(n+1)-a(n) = 2 or 3.
Conjecture: for n>3 a(n) = round(e*n-(1/2)*log(2*Pi*n)-1/n). - Benoit Cloitre, Dec 14 2005
Above conjecture is false: For n = 195 we have: a(n) = 526 < 527 = round(exp(1)*n -(1/2)*log(2*Pi*n)-1/n). - Alois P. Heinz, Jan 15 2022
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MAPLE
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a:= proc(n) option remember; local k; if n<0 then 1 else
for k from a(n-1) while k! < n^k do od; k fi
end:
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[k! < n^k, k++ ]; k]; Table[ f[n], {n, 62}] (* Robert G. Wilson v, Jun 12 2004 *)
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PROG
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(PARI) a(n)=if(n<2, 1, k=1; while(k!<n^k, k++); k)
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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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STATUS
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approved
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