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
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Sep 03 2006
STATUS
approved