%I A156344
%S A156344 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,
%T A156344 241,27190,2,51,21,11,260,3,1,62,26,14,8,151,2,73,31,17,492,268,3,1,86,
%U A156344 2535,869,315546,1065,183,2,99,43,2226,15,350,294,3,1,114,50,1457,18
%N A156344 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.
%C A156344 We conjecture sequence is never zero.
%F A156344 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.
%o A156344 (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)
%Y A156344 Cf. A002620, A073524
%Y A156344 Sequence in context: A137211 A083855 A062565 this_sequence A119440 A165742 
               A162984
%Y A156344 Adjacent sequences: A156341 A156342 A156343 this_sequence A156345 A156346 
               A156347
%K A156344 nonn
%O A156344 1,2
%A A156344 Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2009