id:A145355 - OEIS Search Results

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a(n)=Round[Sqrt[n! ]/Abs[Round[Sqrt[n! ]]^2 - n! ]]

+0
1

1, 1, 5, 11, 3, 71, 2, 1, 8, 20, 5, 1, 2, 5, 1, 2, 2, 1, 1, 3, 1, 1, 8, 2, 13, 22, 1, 1, 3, 2, 2, 3, 2, 2, 1, 2, 3, 2, 3, 1, 9, 2, 2, 1, 2, 1, 1, 2, 2, 1, 6, 1, 1, 4, 2, 2, 2, 3, 21, 2, 1, 1, 1, 1, 2, 2, 6, 8, 4, 7, 1, 2, 2, 1, 3, 1, 1, 9, 2, 1, 2, 4, 3, 5, 1, 1, 2, 5, 13, 6 (list; graph; listen)

	OFFSET	`2,3`
	COMMENT	This sequence suggests that the distance between a factorial and the closest power is tightly bounded. Generated by Ed Pegg Jr <ed(AT)mathpuzzle.com> in response to three Alexander R. Povolotsky conjectures: 1)n! + n^2 != m^2 (except for trivial case with n=0, m=1) per conducted calculations doesn't yield any solutions from n=1 to n= 200,000 2)n! + Sum(j^2, j=1, j=n) != m^2 per conducted calculations doesn't yield any solutions from n=1 to n= 2,000,000 3)n! + prime(n) != m^k is too difficult to cover by exhaustive calculations ...
	CROSSREFS	`Sequence in context: A100298 A066461 A117069 this_sequence A110353 A097720 A077806` `Adjacent sequences: A145352 A145353 A145354 this_sequence A145356 A145357 A145358`
	KEYWORD	`nonn`
	AUTHOR	`Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 09 2008`

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Last modified December 5 08:23 EST 2009. Contains 170348 sequences.

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