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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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..32. 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. 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 Cf. A002034, A007677. Sequence in context: A060023 A345531 A357644 * A114210 A073271 A117471 Adjacent sequences: A120352 A120353 A120354 * A120356 A120357 A120358 KEYWORD hard,more,nonn AUTHOR Jonathan Sondow, Aug 16 2006 EXTENSIONS Extended by Max Alekseyev, Jul 28 2009 STATUS approved

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Last modified December 1 15:57 EST 2023. Contains 367485 sequences. (Running on oeis4.)