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A087793
Least k such that S^k(n)=n^2 where S(x)=n*ceiling(sqrt(x)).
0
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
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Oct 07 2003
STATUS
approved