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A000227
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Nearest integer to e^n.
(Formerly M2678 N1071)
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14
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1, 3, 7, 20, 55, 148, 403, 1097, 2981, 8103, 22026, 59874, 162755, 442413, 1202604, 3269017, 8886111, 24154953, 65659969, 178482301, 485165195, 1318815734, 3584912846, 9744803446, 26489122130, 72004899337, 195729609429, 532048240602, 1446257064291, 3931334297144, 10686474581524
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OFFSET
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0,2
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COMMENTS
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x = e^n is the location of the maximum of x^(1/x^(1/n)). One can define another sequence, c(n) as the value of the natural number k that maximizes k^(1/k^(1/n)). Empirically, despite the rounding, c(n) and a(n) match each other until at least n>24500 (see the link). - Stanislav Sykora, Jun 06 2014
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REFERENCES
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Federal Works Agency, Work Projects Administration for the City of NY, Tables of the Exponential Function. National Bureau of Standards, Washington, DC, 1939.
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 230.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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Digits := 40: [seq(round(exp(n)), n=0..30)];
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MATHEMATICA
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Table[ Round[ N[E^n] ], {n, 0, 30} ]
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PROG
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(PARI) apply( A000227(n)=exp(n)\/1, [0..50]) \\ An error message will say so if default(realprecision) must be increased. - M. F. Hasler, May 27 2018
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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