A079490 Exp(n) is closer to an integer than any previous exp(k) for 1 <= k < n.

1, 3, 8, 19, 45, 75, 135, 178, 209, 732, 1351, 1907, 5469, 28414, 37373, 404055, 902497

Offset

1,2

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 178, p. 56, Ellipses, Paris 2008.

Links

Table of n, a(n) for n=1..17.

Example

a(2) = 3: exp(3) = 20.08... is closer to an integer than exp(1) = 2.718...
At 37373 the difference from an integer is 0.0000010493779591646530966...

Mathematica

a = 1; Do[ d = Abs[ Round[E^n] - N[E^n, Ceiling[ Log[10, E^n] + 10]]]; If[d < a, Print[n]; a = d], {n, 1, 50000}]

Prog

(PARI) {default(realprecision, 1000); d(x)=abs(x-round(x))}; a(n)=local(m); if(n<2, n>0, n=a(n-1); m=d(exp(n)); until(d(exp(n))<m, n++); n)
(PARI) d(x)=x=frac(x); min(x, 1-x)
D(n)=localbitprec(n/log(2)+99); d(exp(n))
r=1; for(n=1, 4e4, t=D(n); if(t<r, r=t; print1(n", "))) \\ Charles R Greathouse IV, Oct 31 2022

Crossrefs

Cf. A000149, A001671, A004790, A080053.

Sequence in context: A281812 A077850 A097550 * A361506 A026789 A308372

Adjacent sequences: A079487 A079488 A079489 * A079491 A079492 A079493

Keyword

nonn,more

Author

Donald S. McDonald, Jan 20 2003

Extensions

Corrected and extended to 1351 by several correspondents, Jan 20 2003

a(12)-a(15) from Robert G. Wilson v, Jan 20 2003

a(16)-a(17) from Charles R Greathouse IV, Nov 01 2022

Status

approved