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A007677
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Denominators of convergents to e.
(Formerly M2343)
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16
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1, 1, 3, 4, 7, 32, 39, 71, 465, 536, 1001, 8544, 9545, 18089, 190435, 208524, 398959, 4996032, 5394991, 10391023, 150869313, 161260336, 312129649, 5155334720, 5467464369, 10622799089, 196677847971, 207300647060, 403978495031, 8286870547680, 8690849042711
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OFFSET
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1,3
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COMMENTS
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Same as A113874 without its first two terms. - Jonathan Sondow, Aug 16 2006
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REFERENCES
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E. B. Burger, Diophantine Olympics ..., Amer. Math. Monthly, 107 (Nov. 2000), 822-829.
CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 88.
W. J. LeVeque, Fundamentals of Number Theory. Addison-Wesley, Reading, MA, 1977, p. 240.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.
Eric Weisstein's World of Mathematics, e.
Eric Weisstein's World of Mathematics, Sultan's Dowry Problem
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MAPLE
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Digits := 60: E := exp(1); convert(evalf(E), confrac, 50, 'cvgts'): cvgts;
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MATHEMATICA
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Denominator[Convergents[E, 40]] (* T. D. Noe, Oct 12 2011 *)
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CROSSREFS
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Cf. A007676.
Sequence in context: A041091 A117764 A113874 * A042773 A042173 A046461
Adjacent sequences: A007674 A007675 A007676 * A007678 A007679 A007680
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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STATUS
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approved
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