id:A102730 - OEIS Search Results

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Number of factorials contained in n! in binary representation.

+0
13

1, 2, 3, 4, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 8, 6, 7, 6, 7, 6, 7, 7, 7, 8, 7, 7, 7, 6, 8, 7, 7, 7, 7, 7, 8, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 8, 8, 7, 7, 7, 8, 8, 7, 8, 7, 7 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`Conjecture: the sequence is bounded.` `For n>0: A103670(n) = smallest m such that a(m)=n;` `A103671(n) = smallest m such that in binary representation n! doesn't contain m!;` `A103672(n) = greatest m less than n such that in binary representation n! contains m!.`
	LINKS	`Index entries for sequences related to factorial numbers.` `Index entries for sequences related to binary expansion of n`
	EXAMPLE	`n=6: 6!=720->'1011010000' contains a(6)=5 factorials: 0!=1->'1', 1!=1->'1', 2!=2->'10', 3!=6->'110' and 6! itself, but not 4!=24->'11000' and 5!=120->'1111000'.`
	CROSSREFS	`Cf. A036603, A007088, A000142, A011371, A093684.` `Cf. A103673, A103676, A103677, A103674, A103678, A103679, A103675, A103680, A103681.` `Sequence in context: A094700 A073635 A071532 this_sequence A165597 A099033 A002330` `Adjacent sequences: A102727 A102728 A102729 this_sequence A102731 A102732 A102733`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 07 2005`

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Last modified December 8 08:31 EST 2009. Contains 170430 sequences.

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