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A120355
a(n) = min{k>0: the n-th convergent to e equals m/k! for some m}.
0
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
0,3
LINKS
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.
FORMULA
a(n) = A002034(A007677(n)).
EXAMPLE
The 6th convergent to e is 87/32 and 32 divides 8! but not 7!, so a(6) = 8.
CROSSREFS
Sequence in context: A060023 A345531 A357644 * A114210 A073271 A117471
KEYWORD
hard,more,nonn
AUTHOR
Jonathan Sondow, Aug 16 2006
EXTENSIONS
Extended by Max Alekseyev, Jul 28 2009
Missing a(7)=71 inserted by Georg Fischer, Oct 15 2024
STATUS
approved