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A095822
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Numerators of certain upper bounds for Euler's number e.
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2
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3, 11, 49, 87, 1631, 11743, 31967, 876809, 8877691, 4697191, 1193556233, 2232105163, 2222710781, 3317652307271, 53319412081141, 303328210950491, 2348085347268533, 313262209859119579, 42739099682215483
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For the denominators see A095823.
e:=sum(1/k!,k=0..infty) has (trivial) upper bound r(n):= a(n)/A095823(n). See the W. Lang link.
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REFERENCES
| M. Barner and F. Flohr, Analysis I, de Gruyter, 5te Auflage, 2000; pp. 117/8.
E. Kuz'min and A. I. Shirshov: On the number e, pp. 111-119, eq.(6), in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, Am.Math.Soc., 1999
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LINKS
| W. Lang, r(n) numbers and comments.
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FORMULA
| a(n)= numerator(r(n)), with rational r(n):= sum(1/k!, k=0..n) + 1/(n*n!), n>=1, written in lowest terms. For n*n! see A001563(n).
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EXAMPLE
| The positive rationals r(n), n>=1: 3/1, 11/4, 49/18, 87/32, 1631/600, 11743/4320, 31967/11760, ...
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CROSSREFS
| Sequence in context: A187249 A105151 A111680 * A025539 A172440 A074528
Adjacent sequences: A095819 A095820 A095821 * A095823 A095824 A095825
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KEYWORD
| nonn,easy,frac
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jun 11 2004
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