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Search: id:A079490
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| A079490 |
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Exp(n) is closer to an integer than any previous exp(k) for 1 <= k < n. |
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+0
12
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| 1, 3, 8, 19, 45, 75, 135, 178, 209, 732, 1351, 1907, 5469, 28414, 37373
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 178, p. 56, Ellipses, Paris 2008.
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EXAMPLE
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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...
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MATHEMATICA
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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}]
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PROGRAM
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(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))<m, n++); n)
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CROSSREFS
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Cf. A000149, A001671, A004790, A080053.
Sequence in context: A121551 A077850 A097550 this_sequence A026789 A096576 A126874
Adjacent sequences: A079487 A079488 A079489 this_sequence A079491 A079492 A079493
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KEYWORD
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nonn
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AUTHOR
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Donald S. McDonald (don.mcdonald(AT)paradise.net.nz), Jan 20 2003
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EXTENSIONS
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Corrected and extended to 1351 by several correspondents, Jan 20 2003
Four further terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 20 2003
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