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A085830
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Least number k such that (10^n)^k < k!.
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2
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2, 25, 269, 2714, 27177, 271822, 2718274, 27182809, 271828173, 2718281817, 27182818272, 271828182832, 2718281828444, 27182818284575, 271828182845887, 2718281828459027, 27182818284590433, 271828182845904503
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OFFSET
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0,1
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COMMENTS
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A085830(n) = A065027(10^n). This should confirm that the lim n -> infinity of A065027(n)/n -> e from below.
a(63) differs from the Floor(10^63* e) by only 33.
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LINKS
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Table of n, a(n) for n=0..17.
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MATHEMATICA
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LogBaseBStirling[b_, n_] := Block[{}, N[ Log[b, 2*Pi*n]/2 + n*Log[b, n/E] + Log[b, 1 + 1/(12n) + 1/(288n^2) - 139/(51840n^3) - 571/(2488320n^4) + 163879/(209018880n^5)], 64]]; f[0] = 2; f[n_] := f[n] = Block[{k = 10*g[n - 1]}, While[ LogBaseBStirling[10^n, k] <= k, k++ ]; k]; Table[ f[n], {n, 1, 18}]
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CROSSREFS
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Cf. A065027, A011544.
Sequence in context: A229975 A174970 A249893 * A270346 A212022 A198710
Adjacent sequences: A085827 A085828 A085829 * A085831 A085832 A085833
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v, Jul 13 2003
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STATUS
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approved
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