This site is supported by donations to The OEIS Foundation.



110 people attended OEIS-50 (videos, suggestions); annual fundraising drive to start soon (donate); editors, please edit! (stack is over 300), your editing is more valuable than any donation.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094007 Numbers n such that the denominator of the n-th convergent of the continued fraction expansion of e is prime. 4
3, 5, 8, 14, 20, 35, 41, 65, 239, 269 (list; graph; refs; listen; history; text; internal format)



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))).


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).


Table of n, a(n) for n=1..10.

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.


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.


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)


Cf. A000040, A000720, A007677, A094008, A102049.

Sequence in context: A095223 A070948 A141739 * A159914 A153251 A229167

Adjacent sequences:  A094004 A094005 A094006 * A094008 A094009 A094010




Jonathan Sondow, Apr 20 2004; corrected Apr 21, 2004


More terms from Robert G. Wilson v, May 14 2004



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified October 31 12:07 EDT 2014. Contains 248864 sequences.