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A156344 Number of steps to reach a square starting from n and iterating the map: x -> x*ceiling(sqrt(x))/floor(sqrt(x)) or zero if no square is reached. 0
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We conjecture sequence is never zero.

LINKS

Table of n, a(n) for n=1..68.

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 + ceiling((n-1)^2/2) and then the square reached is (floor(n^2/4)+1)^2.

MATHEMATICA

Table[Length[NestWhileList[# Ceiling[Sqrt[#]]/Floor[Sqrt[#]]&, n, !IntegerQ[ Sqrt[#]]&]], {n, 70}] (* Harvey P. Dale, Oct 23 2016 *)

PROG

(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: A083855 A062565 A175137 * A218796 A119440 A165742

Adjacent sequences:  A156341 A156342 A156343 * A156345 A156346 A156347

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 08 2009

STATUS

approved

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Last modified May 11 06:28 EDT 2021. Contains 343784 sequences. (Running on oeis4.)