id:A156344 - OEIS Search Results

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Number of steps to reach a square starting from n and iterating the map: x->x*ceil(sqrt(x))/floor(sqrt(x)) or zero if no square is reached.

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1, 2, 3, 1, 6, 2, 9, 3, 1, 14, 103, 2, 19, 7, 3, 1, 26, 10, 105, 2, 33, 13, 312, 3, 1, 42, 691, 241, 27190, 2, 51, 21, 11, 260, 3, 1, 62, 26, 14, 8, 151, 2, 73, 31, 17, 492, 268, 3, 1, 86, 2535, 869, 315546, 1065, 183, 2, 99, 43, 2226, 15, 350, 294, 3, 1, 114, 50, 1457, 18 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`We conjecture sequence is never zero.`
	FORMULA	`a(k^2)=1, a(k(k+1))=2, a(k(k+2))=3, and less trivially it appears a(floor(n^2/4)+1)=1+ceil((n-1)^2/2) and then the square reached is (floor(n^2/4)+1)^2.`
	PROGRAM	`(PARI) a(n)=if(n<0, 0, s=n; c=1; while(frac(sqrt(s))>0, s=s*ceil(sqrt(s))/floor(sqrt(s)); c++); c)`
	CROSSREFS	`Cf. A002620, A073524` `Sequence in context: A137211 A083855 A062565 this_sequence A119440 A165742 A162984` `Adjacent sequences: A156341 A156342 A156343 this_sequence A156345 A156346 A156347`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2009`

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

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