

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
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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..28.
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)! = A122416(n)!.


EXAMPLE

a(6) = (S(6)+1)! = (3+1)! = 24.


CROSSREFS

Cf. A001113, A002034, A092495, A122416.
Sequence in context: A047890 A071088 A177533 * A321008 A033644 A212309
Adjacent sequences: A122414 A122415 A122416 * A122418 A122419 A122420


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Sep 03 2006


STATUS

approved



