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A122417 Factorials from an irrationality measure for e, with a(1) = 2.

%I A122417 #20 Dec 04 2018 12:04:39
%S A122417 2,6,24,120,720,24,40320,120,5040,720,479001600,120,87178291200,40320,
%T A122417 720,5040,6402373705728000,5040,2432902008176640000,720,40320,
%U A122417 479001600,620448401733239439360000,120,39916800,87178291200,3628800,40320
%N A122417 Factorials from an irrationality measure for e, with a(1) = 2.
%C A122417 If n > 1, then a(n) is the smallest factorial such that |e - m/n| > 1/a(n) for any integer m.
%C A122417 a(n) is the second smallest factorial divisible by n.
%H A122417 Mohammad K. Azarian, <a href="http://www.m-hikari.com/ijcms/ijcms-2012/21-24-2012/azarianIJCMS21-24-2012.pdf">Euler's Number Via Difference Equations</a>, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, No. 22, pp. 1095 - 1102.
%H A122417 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 A122417 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 A122417 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers.</a>
%F A122417 a(n) = (A002034(n)+1)! = A122416(n)!.
%e A122417 a(6) = (S(6)+1)! = (3+1)! = 24.
%t A122417 nmax = 28;
%t A122417 Do[m = 1; While[!IntegerQ[m!/n], m++]; a[n] = (m+1)!, {n, 1, nmax}];
%t A122417 Array[a, nmax] (* _Jean-François Alcover_, Dec 04 2018 *)
%Y A122417 Cf. A001113, A002034, A092495, A122416.
%K A122417 nonn
%O A122417 1,1
%A A122417 _Jonathan Sondow_, Sep 03 2006