A087793 Least k such that S^k(n)=n^2 where S(x)=n*ceiling(sqrt(x)).

0, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 6, 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, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

0,2

Comments

For all m>k, S^m(n)=n^2

Links

Table of n, a(n) for n=0..93.

Formula

a(n)=sqrt(n)+o(sqrt(n))

Prog

(PARI) a(n)=if(n<0, 0, z=1; c=0; while(abs(z-n^2)>0, z=n*ceil(sqrt(z)); c++); c)

Crossrefs

Sequence in context: A305233 A130242 A130245 * A030411 A194817 A211675

Adjacent sequences: A087790 A087791 A087792 * A087794 A087795 A087796

Keyword

nonn

Author

Benoit Cloitre, Oct 07 2003

Status

approved