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 A122416 Numbers from an irrationality measure for e, with a(1) = 2. 4
 2, 3, 4, 5, 6, 4, 8, 5, 7, 6, 12, 5, 14, 8, 6, 7, 18, 7, 20, 6, 8, 12, 24, 5, 11, 14, 10, 8, 30, 6, 32, 9, 12, 18, 8, 7, 38, 20, 14, 6, 42, 8, 44, 12, 7, 24, 48, 7, 15, 11, 18, 14, 54, 10, 12, 8, 20, 30, 60, 6, 62, 32, 8, 9, 14, 12, 68, 18, 24, 8, 72, 7, 74, 38, 11, 20, 12, 14, 80, 7, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If n > 1, then a(n)! is the smallest factorial such that |e - m/n| > 1/a(n)! for any integer m. a(n)! is the second smallest factorial divisible by n. LINKS Mohammad K. Azarian, Euler's Number Via Difference Equations, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, No. 22, pp. 1095 - 1102. 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, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010. FORMULA a(n) = A002034(n) + 1. EXAMPLE a(6) = S(6) + 1 = 3 + 1 = 4. MATHEMATICA nmax = 100; Do[m=1; While[!IntegerQ[m!/n], m++]; a[n] = m+1, {n, 1, nmax}]; Array[a, nmax] (* Jean-François Alcover, Dec 04 2018 *) CROSSREFS Cf. A001113, A002034, A092495, A122417. Sequence in context: A097751 A070667 A245349 * A134665 A271832 A063260 Adjacent sequences:  A122413 A122414 A122415 * A122417 A122418 A122419 KEYWORD nonn AUTHOR Jonathan Sondow, Sep 03 2006 STATUS approved

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Last modified February 21 15:31 EST 2019. Contains 320374 sequences. (Running on oeis4.)