A120355 - OEIS

%I #19 Oct 16 2024 00:01:46

%S 1,1,3,4,7,8,13,71,31,67,13,89,83,18089,5441,17377,36269,26021,4909,

%T 10391023,1097,28879,1846921,519691,1329313,793279,7553783,3308341,

%U 65676881,662407,677311,2425388512913,4403182913,10832561

%N a(n) = min{k>0: the n-th convergent to e equals m/k! for some m}.

%H J. Sondow, <a href="http://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, <a href="http://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.

%H J. Sondow and K. Schalm, <a href="http://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.

%F a(n) = A002034(A007677(n)).

%e The 6th convergent to e is 87/32 and 32 divides 8! but not 7!, so a(6) = 8.

%Y Cf. A002034, A007677.

%K hard,more,nonn

%O 0,3

%A _Jonathan Sondow_, Aug 16 2006

%E Extended by _Max Alekseyev_, Jul 28 2009

%E Missing a(7)=71 inserted by _Georg Fischer_, Oct 15 2024