The On-Line Encyclopedia of Integer Sequences (OEIS)

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A082528

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

#6 by Russ Cox at Fri Mar 30 18:39:17 EDT 2012

AUTHOR

_Benoit Cloitre (benoit7848c(AT)orange.fr), _, Apr 30 2003

Discussion

Fri Mar 30

18:39

OEIS Server: https://oeis.org/edit/global/216

#5 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

KEYWORD

nonn,new

nonn

AUTHOR

Benoit Cloitre (abmtbenoit7848c(AT)wanadooorange.fr), Apr 30 2003

#4 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

KEYWORD

nonn,new

nonn

AUTHOR

Benoit Cloitre (abcloitreabmt(AT)modulonetwanadoo.fr), Apr 30 2003

#3 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

KEYWORD

nonn,new

nonn

AUTHOR

Benoit Cloitre (abcloitre(AT)wanadoomodulonet.fr), Apr 30 2003

#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

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)

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

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

DATA

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

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.

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.

KEYWORD

nonn

AUTHOR

Benoit Cloitre (abcloitre(AT)wanadoo.fr), Apr 30 2003

STATUS

approved