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
Examples
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...
References
- J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 178, p. 56, Ellipses, Paris 2008.
Programs
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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}] -
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)) -
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
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