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Search: id:A101507
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| A101507 |
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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. |
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+0
2
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| 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
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1,1
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COMMENT
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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.
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EXAMPLE
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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).
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CROSSREFS
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Cf. A101506.
Sequence in context: A088030 A101047 A066491 this_sequence A047176 A037175 A048613
Adjacent sequences: A101504 A101505 A101506 this_sequence A101508 A101509 A101510
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KEYWORD
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more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 20 2004
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