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A082527 Least k such that x(k)=0 where x(1)=n x(k)=k^2*floor(x(k-1)/k^2). 1

%I #6 Mar 30 2012 18:39:17

%S 1,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

%T 5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%U 6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Least k such that x(k)=0 where x(1)=n x(k)=k^2*floor(x(k-1)/k^2).

%F a(n) seems to be asymptotic to (c*n)^(1/3) where c=4.96....

%e If x(1)=3 x(2)=4*floor(3/4)=0 hence a(3)=2, if x(1)=10 x(2)=4*floor(10/4)=2 x(3)=0 hence a(10)=3...

%o (PARI) a(n)=if(n<0,0,s=n; c=1; while(s-s%(c^2)>0,s=s-s%(c^2); c++); c)

%Y Cf. A073047.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Apr 30 2003

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