A122416 Numbers from an irrationality measure for e, with a(1) = 2.

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

Offset: 1

Author

Jonathan Sondow, Sep 03 2006

Keywords

• nonn

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.

Examples

			a(6) = S(6) + 1 = 3 + 1 = 4.
		

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.
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A001113, A002034, A092495, A122417.

Programs

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 *)

Formula

a(n) = A002034(n) + 1.