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Search: id:A094007
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| A094007 |
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Numbers n such that the denominator of the n-th convergent of the continued fraction expansion of e is prime. |
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+0
5
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OFFSET
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1,1
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COMMENT
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a(n) is the position of A094008(n) in A007677 (denominators of convergents to e), so A007677(a(n)) = A094008(n). Also, A102049(n) is the position of A007677(a(n)) in A000040 (the prime numbers), so A000040(A102049(n)) = A007677(a(n))). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 27 2004
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics\.
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EXAMPLE
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The convergents for e are 2, 3, 8/3, 11/4, 19/7, ... and so the 3rd convergent is the first one with prime denominator: a(1) = 3 and the 5th convergent is the 2nd one with prime denominator: a(2) = 5.
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MATHEMATICA
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L = {}; cf = ContinuedFraction[E, 5000]; Do[ If[ PrimeQ[ Denominator[ FromContinuedFraction[ Take[ cf, n]] ]], AppendTo[L, n]], {n, Length[cf]}]; L (from Robert G. Wilson v)
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CROSSREFS
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Cf. A000040, A000720, A007677, A094008, A102049.
Sequence in context: A095223 A070948 A141739 this_sequence A159914 A153251 A109022
Adjacent sequences: A094004 A094005 A094006 this_sequence A094008 A094009 A094010
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KEYWORD
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nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Apr 20 2004; corrected Apr 21, 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 14 2004
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