

A101507


Numbers n such that exp(n) has a smaller relative error abs(exp(n)/m!1) in approximating the closest factorial m!>1 than exp(k) for any k with 1<k<n.


1



2, 3, 15, 20, 58, 2893, 3172, 13778, 36596, 63894, 208744, 296557, 404667, 11500740, 17800369, 37858613, 38393813, 902477623, 4126573365, 79491128275, 338814192247, 1599109448865
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OFFSET

1,1


COMMENTS

Numbers n such that abs(exp(n)/m!1)<abs(exp(k)/j!1) with m such that abs(exp(n)m!)=min for any k with 1<k<n and j such that abs(exp(k)j!)=min.


LINKS



EXAMPLE

a(1)=2 because exp(2)=7.389 is a better approximation to the nearest factorial 3!=6 with +23% relative error than is exp(1)=2.718 for its closest factorial 2!=2 with +36% relative error.
a(2)=3: exp(3)/4!1=0.1631. The next improvement occurs for a(3)=15 because exp(15)/10!1=0.099.
a(22)=1599109448865: The relative error of exp(1599109448865) in approximating A101506(22)!=66836971558! is 1.276*10^(12).


CROSSREFS



KEYWORD

more,nonn


AUTHOR



STATUS

approved



