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

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

Offset: 1

Author

Hugo Pfoertner, Dec 20 2004

Keywords

• more
• nonn

Comments

Numbers n such that abs(exp(n)/m!-1)

Examples

			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.

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