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A102049
Indices of primes which are denominators of convergents to e.
2
2, 4, 20, 2073, 688812, 23493068282804, 51287550456151700
OFFSET
1,1
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))).
a(6)-a(7) computed using Kim Walisch's primecount program. - Giovanni Resta, Jun 03 2019
LINKS
E. B. Burger, Diophantine Olympics and World Champions: Polynomials and Primes Down Under, 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).
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; arXiv:0709.0671 [math.NT], 2007-2009.
Eric Weisstein's World of Mathematics, e.
FORMULA
a(n) = A000720(A094008(n)).
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jonathan Sondow, Dec 27 2004
EXTENSIONS
a(6)-a(7) from Giovanni Resta, Jun 03 2019
STATUS
approved