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A247781
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Least k such that 1/e - (1 - 1/k)^k < 1/n.
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3
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1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15
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OFFSET
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1,3
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COMMENTS
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a(n+1) - a(n) is in {0,1} for n >= 1.
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LINKS
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EXAMPLE
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The values of 1/e - (1 - 1/k)^k for n = 1..9 are approximately 0.367879, 0.117879, 0.0715831, 0.0514732, 0.0401994, 0.0329815, 0.0279628, 0.0242705, 0.02144, from which we see that the first 9 terms of A247781 are 1, 1, 2, 2, 2, 2, 2, 2, 3.
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MATHEMATICA
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z = 400; f[n_] := f[n] = Select[Range[z], 1/E - (1 - 1/#)^# < 1/n &, 1];
u = Flatten[Table[f[n], {n, 1, z}]] (*A247781*)
d1 = Flatten[Position[Differences[u], 0]] (*A247782*)
d2 = Flatten[Position[Differences[u], 1]] (*A247783*)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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