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.

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

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

Table of n, a(n) for n=1..22.

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

Cf. A101506.

Sequence in context: A331089 A294131 A274003 * A047176 A347668 A325236

Adjacent sequences: A101504 A101505 A101506 * A101508 A101509 A101510

Keyword

more,nonn

Author

Hugo Pfoertner, Dec 20 2004

Status

approved