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A056155
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Positive integer k, 1 <= k <= n, which maximizes k^(n+1-k).
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3
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1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20
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OFFSET
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1,2
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COMMENTS
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a(n) is within 1 of x, where n+1 = x*(1 + log(x)).
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LINKS
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FORMULA
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a(n) ~ e^(LambertW(e*(n + 1)) - 1). - Mats Granvik, Jan 26 2017
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EXAMPLE
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a(5) = 3 because 3^(5+1-3) = 27 is larger than k^(5+1-k) for any other k (1 <= k <= n) besides k = 3.
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MATHEMATICA
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nn = 79; Monitor[a = Table[RankedMax[Table[k^(n + 1 - k), {k, 1, n}], 1], {n, 1, nn}]; , n] Monitor[b = Flatten[Table[Position[Table[k^(n + 1 - k), {k, 1, n}], a[[n]]], {n, 1, nn}]], n] (* Mats Granvik, Jan 26 2017 *)
a[n_] := MaximalBy[Range[n], #^(n + 1 - #)&][[1]];
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PROG
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(PARI) a(n) = my(v = vector(n, k, k^(n+1-k))); vecsort(v, , 1)[#v]; \\ Michel Marcus, Jan 28 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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