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A066661
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Numbers m such that floor((1+1/m)^k)=k for an integer k>1.
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1
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2, 3, 4, 5, 7, 13, 20, 27, 31, 34, 36, 38, 48, 65, 70, 73, 76, 79, 95, 104, 112, 117, 125, 126, 144, 145, 153, 154, 159, 164, 172, 179, 182, 185, 190, 195, 202, 204, 216, 218, 225, 235, 253, 269, 279, 285, 291, 292, 300, 301, 313, 314, 315, 340, 341, 342, 355, 356, 365
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OFFSET
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1,1
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LINKS
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FORMULA
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Conjecture: a(n)=C*n*log(n) asymptotically with C=1.5...
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EXAMPLE
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Floor((1+1/4)^11) = 11 hence 4 is in the sequence.
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MATHEMATICA
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t = Table[Floor[Re[-LambertW[-1, -Log[1 + 1/n]]/Log[1 + 1/n]] + 1], {n, 1, 1000}]; Select[Range[Length[t]], Floor[(1 + 1/#1)^t[[#1]]] == t[[#1]]&] (* Vaclav Kotesovec, Feb 16 2019 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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