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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 (list; graph; refs; listen; history; text; internal format)
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) 637-641.

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 * A033644 A212309 A232983

Adjacent sequences:  A122414 A122415 A122416 * A122418 A122419 A122420

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Sep 03 2006

STATUS

approved

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Last modified May 26 12:58 EDT 2017. Contains 287095 sequences.