id:A122417 - OEIS Search Results

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

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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; listen)

	OFFSET	`1,1`
	COMMENT	`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	`J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.`
	LINKS	`I ndex entries for sequences related to factorial numbers.`
	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: A052398 A047890 A071088 this_sequence A033644 A154654 A070947` `Adjacent sequences: A122414 A122415 A122416 this_sequence A122418 A122419 A122420`
	KEYWORD	`nonn`
	AUTHOR	`Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Sep 03 2006`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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