OFFSET
1,1
COMMENTS
Length of n-th run of consecutive identical terms is given by A028913 - Ralf Stephan.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Presumably a(n) = sqrt(Pi*n)+O(1).
EXAMPLE
If x(1)=4, x(2)= 2*floor(4/2)=4, x(3)=3*floor(4/3)=3; x(4)=4*floor(3/4)=0 hence a(4)=4.
MAPLE
f:= proc(n, k) option remember;
if n = 0 then return k-1 fi;
procname(k*floor(n/k), k+1)
end proc:
map(f, [$1..100], 1); # Robert Israel, Jul 25 2019
MATHEMATICA
a[n_] := Module[{x}, x[1] = n; x[k_] := x[k] = k Floor[x[k-1]/k]; For[k = 1, True, k++, If[x[k] == 0, Return[k]]]];
Array[a, 100] (* Jean-François Alcover, Jun 07 2020 *)
PROG
(PARI) a(n)=if(n<0, 0, s=n; c=1; while(s-s%c>0, s=s-s%c; c++); c)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 31 2002; revised May 03 2003
STATUS
approved