A082528 - OEIS

A082528

Least k such that x(k)=0 where x(1)=n x(k)=k^3*floor(x(k-1)/k^3).

1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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OFFSET

0,2

COMMENTS

Conjecture : define sequence a(n,m) m real >0 as the least k such that x(k)=0 where x(1)=n x(k)=k^m*floor(x(k-1)/k^m) then a(n,m) is asymptotic to (c(m)*n)^(1/(m+1)). where c(m) is a constant depending on m.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

a(n) seems to be asymptotic to (c*n)^(1/4) where c=6.76....

PROG

(PARI) a(n)=if(n<0, 0, s=n; c=1; while(s-s%(c^3)>0, s=s-s%(c^3); c++); c)

CROSSREFS

Cf. A073047.

Sequence in context: A232270 A191517 A303370 * A055980 A076080 A134914

Adjacent sequences: A082525 A082526 A082527 * A082529 A082530 A082531

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 30 2003

STATUS

approved