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A000227 Nearest integer to e^n.
(Formerly M2678 N1071)
14
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 (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
Stanislav Sykora, Comments on A000227
MAPLE
Digits := 40: [seq(round(exp(n)), n=0..30)];
MATHEMATICA
Table[ Round[ N[E^n] ], {n, 0, 30} ]
PROG
(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
CROSSREFS
Cf. A000149 (floor e^n), A001671 (e^n rounded up), A002160 (nearest integer to Pi^n).
Sequence in context: A293740 A293110 A322204 * A327993 A245891 A058737
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified March 28 16:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)