A120355 a(n) = min{k>0: the n-th convergent to e equals m/k! for some m}.
1, 1, 3, 4, 7, 8, 13, 71, 31, 67, 13, 89, 83, 18089, 5441, 17377, 36269, 26021, 4909, 10391023, 1097, 28879, 1846921, 519691, 1329313, 793279, 7553783, 3308341, 65676881, 662407, 677311, 2425388512913, 4403182913, 10832561
Offset: 0
Examples
The 6th convergent to e is 87/32 and 32 divides 8! but not 7!, so a(6) = 8.
Links
- 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, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
- 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.
Extensions
Extended by Max Alekseyev, Jul 28 2009
Missing a(7)=71 inserted by Georg Fischer, Oct 15 2024