Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M2678 N1071 #35 May 28 2018 14:22:56
%S 1,3,7,20,55,148,403,1097,2981,8103,22026,59874,162755,442413,1202604,
%T 3269017,8886111,24154953,65659969,178482301,485165195,1318815734,
%U 3584912846,9744803446,26489122130,72004899337,195729609429,532048240602,1446257064291,3931334297144,10686474581524
%N Nearest integer to e^n.
%C 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 Federal Works Agency, Work Projects Administration for the City of NY, Tables of the Exponential Function. National Bureau of Standards, Washington, DC, 1939.
%D 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 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000227/b000227.txt">Table of n, a(n) for n=0..200</a>
%H Stanislav Sykora, <a href="/A000227/a000227.txt">Comments on A000227</a>
%p Digits := 40: [seq(round(exp(n)), n=0..30)];
%t Table[ Round[ N[E^n] ], {n, 0, 30} ]
%o (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 Cf. A000149 (floor e^n), A001671 (e^n rounded up), A002160 (nearest integer to Pi^n).
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_