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 A122417 Factorials from an irrationality measure for e, with a(1) = 2. 4
 2, 6, 24, 120, 720, 24, 40320, 120, 5040, 720, 479001600, 120, 87178291200, 40320, 720, 5040, 6402373705728000, 5040, 2432902008176640000, 720, 40320, 479001600, 620448401733239439360000, 120, 39916800, 87178291200, 3628800, 40320 (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)! = A122416(n)!. EXAMPLE a(6) = (S(6)+1)! = (3+1)! = 24. MATHEMATICA nmax = 28; 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, A122416. Sequence in context: A297204 A071088 A177533 * A321008 A033644 A212309 Adjacent sequences:  A122414 A122415 A122416 * A122418 A122419 A122420 KEYWORD nonn AUTHOR Jonathan Sondow, Sep 03 2006 STATUS approved

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Last modified September 21 09:51 EDT 2019. Contains 327253 sequences. (Running on oeis4.)