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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
OFFSET
1,2
COMMENTS
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 + 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
Sequence in context: A083855 A062565 A175137 * A218796 A119440 A165742
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 08 2009
STATUS
approved