A102049 Indices of primes which are denominators of convergents to e.

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

Offset: 1

Author

Jonathan Sondow, Dec 27 2004

Keywords

• nonn
• more

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

Examples

			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.
		

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, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010.
• 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.

Crossrefs

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

Formula

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

Extensions

a(6)-a(7) from Giovanni Resta, Jun 03 2019