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A000227 Nearest integer to e^n.

%I A000227 M2678 N1071 #37 Jul 28 2025 18:13:13
%S A000227 1,3,7,20,55,148,403,1097,2981,8103,22026,59874,162755,442413,1202604,
%T A000227 3269017,8886111,24154953,65659969,178482301,485165195,1318815734,
%U A000227 3584912846,9744803446,26489122130,72004899337,195729609429,532048240602,1446257064291,3931334297144,10686474581524
%N A000227 Nearest integer to e^n.
%C A000227 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
%D A000227 Federal Works Agency, Work Projects Administration for the City of NY, Tables of the Exponential Function. National Bureau of Standards, Washington, DC, 1939.
%D A000227 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.
%D A000227 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000227 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000227 T. D. Noe, <a href="/A000227/b000227.txt">Table of n, a(n) for n=0..200</a>
%H A000227 Stanislav Sykora, <a href="/A000227/a000227.txt">Comments on A000227</a>
%p A000227 Digits := 40: [seq(round(exp(n)), n=0..30)];
%t A000227 Table[ Round[ N[E^n] ], {n, 0, 30} ]
%t A000227 Round[E^Range[0,30]] (* _Harvey P. Dale_, Jul 28 2025 *)
%o A000227 (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
%Y A000227 Cf. A000149 (floor e^n), A001671 (e^n rounded up), A002160 (nearest integer to Pi^n).
%K A000227 nonn,easy,nice
%O A000227 0,2
%A A000227 _N. J. A. Sloane_