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A102049
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Indices of primes which are denominators of convergents to e.
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2
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OFFSET
| 1,1
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COMMENTS
| The prime denominators of convergents to e form A094008 (so A000040(a(n)) = A094008(n)). Their positions in A007677 (denominators of convergents to e) form A094007, so a(n) = A000720(A007677(A094007(n))).
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REFERENCES
| E. B. Burger, Diophantine Olympics ..., Amer. Math. Monthly, 107 (Nov. 2000), 822-829.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641 (article), 114 (2007) 659 (addendum).
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LINKS
| 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, Link to a section of The World of Mathematics
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FORMULA
| a(n) = A000720(A094008(n)).
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EXAMPLE
| a(1) = 2 because the first convergent to e with prime denominator is 8/3 and the index of 3 is 2, i.e., 3 is the 2nd prime.
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CROSSREFS
| Cf. A000040, A000720, A007677, A094007, A094008.
Sequence in context: A132498 A087314 A099179 * A058522 A122736 A092458
Adjacent sequences: A102046 A102047 A102048 * A102050 A102051 A102052
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KEYWORD
| nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 27 2004
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