A130147 a(0)=1. a(n+1) = a(floor(n/a(n))) + 1.

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

Offset: 0

Author

Leroy Quet, Aug 02 2007

Keywords

• easy
• nonn

Comments

Records occur at 0,1,3,10,41,206,1237,8660,69281,623530,6235301, which appears to be A002627. See A132424 for a related sequence. - John W. Layman, Aug 20 2007

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A002627, A132424.

See A130193 for "ceiling" version.

Programs

Maple

a[0]:=1: for n from 0 to 110 do a[n+1]:=1+a[floor(n/a[n])] end do: seq(a[n],n=0..110); # Emeric Deutsch, Aug 19 2007

Mathematica

a[0] = 1; a[n_] := a[n] = 1 + a[Floor[(n - 1)/a[n - 1]]]; Array[a, 105, 0] (* Michael De Vlieger, Sep 03 2017 *)

Extensions

More terms from Emeric Deutsch and John W. Layman, Aug 19 2007