

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
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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.


REFERENCES

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) 637641.


LINKS

Table of n, a(n) for n=1..81.
Index entries for sequences related to factorial numbers.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality


FORMULA

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


EXAMPLE

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


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



