id:A081885 - OEIS Search Results

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Number of steps needed to reach an integer starting with n+1/16 and iterating the map x-->x*ceiling(x).

+0
1

8, 5, 3, 8, 18, 8, 5, 6, 5, 6, 3, 6, 7, 5, 1, 6, 4, 6, 3, 4, 2, 6, 2, 7, 3, 2, 4, 6, 2, 5, 1, 8, 12, 4, 7, 4, 8, 7, 3, 9, 10, 5, 3, 9, 5, 6, 1, 3, 11, 4, 2, 4, 4, 4, 2, 4, 6, 7, 2, 2, 5, 3, 1, 7, 9, 9, 5, 7, 4, 13, 4, 5, 6, 8, 6, 14, 8, 3, 1, 4, 2, 5, 4, 5, 3, 2, 2, 10, 2, 5, 3, 18, 4, 3, 1, 11, 4, 7, 7, 4, 5 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Conjecture : let b(n,m) denotes the number of steps needed to reach an integer starting with n+1/2^m and iterating the map x-->xceiling(x); then sum(k=1,n,b(k,m)) is asymptotic to (m+1)n.`
	FORMULA	`It seems that sum(k=1, n, a(k)) is asymptotic to 5n.`
	PROGRAM	`(PARI) a(n)=if(n<0, 0, s=n+1/16; c=0; while(frac(s)>0, s=s*ceil(s); c++); c)`
	CROSSREFS	`Cf. A068119, A073524.` `Sequence in context: A086723 A011406 A011466 this_sequence A019609 A093341 A134973` `Adjacent sequences: A081882 A081883 A081884 this_sequence A081886 A081887 A081888`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2003`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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