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A000227 Nearest integer to e^n.
(Formerly M2678 N1071)
7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

Stanislav Sykora, Comments on A000227

MAPLE

Digits := 40: [seq(round(exp(n)), n=0..30)];

MATHEMATICA

Table[ Round[ N[E^n] ], {n, 0, 30} ]

CROSSREFS

Cf. A002581, A243443.

Sequence in context: A003097 A109220 A018034 * A245891 A058737 A274478

Adjacent sequences:  A000224 A000225 A000226 * A000228 A000229 A000230

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Apr 30 1991

STATUS

approved

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Last modified March 23 19:17 EDT 2017. Contains 283957 sequences.