A102049 - OEIS

%I #19 Jun 03 2019 09:53:18

%S 2,4,20,2073,688812,23493068282804,51287550456151700

%N Indices of primes which are denominators of convergents to e.

%C 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))).

%C a(6)-a(7) computed using Kim Walisch's primecount program. - _Giovanni Resta_, Jun 03 2019

%H E. B. Burger, <a href="https://www.jstor.org/stable/2695737">Diophantine Olympics and World Champions: Polynomials and Primes Down Under</a>, Amer. Math. Monthly, 107 (Nov. 2000), 822-829.

%H J. Sondow, <a href="https://www.jstor.org/stable/27642006">A geometric proof that e is irrational and a new measure of its irrationality</a>, Amer. Math. Monthly 113 (2006) 637-641 (article), 114 (2007) 659 (addendum).

%H J. Sondow, <a href="https://arxiv.org/abs/0704.1282"> A geometric proof that e is irrational and a new measure of its irrationality</a>, arXiv:0704.1282 [math.HO], 2007-2010.

%H J. Sondow and K. Schalm, <a href="https://arxiv.org/abs/0709.0671">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</a>, 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/e.html">e</a>.

%F a(n) = A000720(A094008(n)).

%e 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.

%Y Cf. A000040, A000720, A007677, A094007, A094008.

%K nonn,more

%O 1,1

%A _Jonathan Sondow_, Dec 27 2004

%E a(6)-a(7) from _Giovanni Resta_, Jun 03 2019