A014015 Denominators of sign-alternating Egyptian fraction expansion of e - 2.

1, 3, 19, 983, 1140455, 25739184407616, 687786653376698575362597850, 531547061991816754123214108000546228669815660470108834

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Comments

The greedy alternating Egyptian fraction for e-2 must begin with 1/1 as the (-1)^0 term. - Greg Huber, May 17 2018

a(n) >= a(n-1)^2 + a(n-1) for n >= 1, so the ratio log(a(n))/2^n is strictly increasing. But does it approach a limit? Conjecture: lim_{n->infinity} log(a(n))/2^n = 0.9748... - Jon E. Schoenfield, Jun 22 2018

Links

• Greg Huber, Table of n, a(n) for n = 0..8
• Index entries for sequences related to Egyptian fractions

Extensions

Initial 2 removed, offset corrected and Name clarified by Greg Huber, May 17 2018