A073047 Least k such that x(k)=0 where x(1)=n and x(k)=k*floor(x(k-1)/k).

2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16

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

Cf. A002491, A007952, A082527, A082528.

Sequence in context: A341053 A126236 A198194 * A038567 A185195 A192512

Adjacent sequences: A073044 A073045 A073046 * A073048 A073049 A073050

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 31 2002; revised May 03 2003

Status

approved