id:A081884 - OEIS Search Results

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Number of steps needed to reach an integer starting with n+1/8 and iterating the map x-->x*ceiling(x).

+0
1

4, 7, 4, 7, 7, 6, 1, 3, 2, 2, 2, 7, 2, 3, 1, 6, 5, 4, 3, 7, 7, 6, 1, 3, 3, 5, 2, 2, 3, 3, 1, 5, 3, 9, 6, 4, 7, 3, 1, 3, 2, 3, 2, 3, 2, 2, 1, 5, 5, 4, 3, 10, 3, 4, 1, 2, 4, 5, 2, 7, 7, 9, 1, 6, 6, 3, 4, 12, 3, 13, 1, 5, 2, 2, 2, 10, 2, 5, 1, 5, 3, 13, 3, 3, 5, 6, 1, 9, 3, 6, 2, 2, 3, 4, 1, 6, 6, 6, 5, 6, 4, 4, 1 (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 4n.`
	PROGRAM	`(PARI) a(n)=if(n<0, 0, s=n+1/8; c=0; while(frac(s)>0, s=s*ceil(s); c++); c)`
	CROSSREFS	`Cf. A068119, A073524.` `Sequence in context: A106739 A112677 A010712 this_sequence A059143 A094765 A021682` `Adjacent sequences: A081881 A081882 A081883 this_sequence A081885 A081886 A081887`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2003`

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Last modified December 20 00:58 EST 2009. Contains 171054 sequences.

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