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A094008
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Primes which are the denominators of convergents of the continued fraction expansion of e.
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4
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OFFSET
| 1,1
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COMMENTS
| The position of a(n) in A000040 (the prime numbers) is A102049(n) = A000720(a(n)). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 27 2004
The next term has 166 digits. [From Harvey P. Dale, Aug 23 2011]
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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
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics\.
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FORMULA
| a(n) = A007677(A094007(n)) = A000040(A102049(n)).
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EXAMPLE
| a(1) = 3 because 3 is the first prime denominator of a convergent, 8/3, of the simple continued fraction for e
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MATHEMATICA
| Block[{$MaxExtraPrecision=1000}, Select[Denominator[Convergents[E, 500]], PrimeQ]] (* From Harvey P. Dale, Aug 23 2011 *)
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CROSSREFS
| Cf. A094007. See also A000040, A000720, A007677, A102049.
Sequence in context: A127179 A113841 A128072 * A078552 A091259 A088647
Adjacent sequences: A094005 A094006 A094007 * A094009 A094010 A094011
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KEYWORD
| nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Apr 20 2004
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