A137735 a(0)=1. a(n) = floor(n/b(n)), where b(n) is the largest value among (a(0),a(1),...,a(n-1)).

1, 1, 2, 1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10

Offset

0,3

Comments

Length of n-th run appears to be A103627(n + 2) for n > 1. - Peter Kagey, Apr 25 2016

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Formula

For all m>=1, a(k) = m if m^2 <= k <= m^2 +m-1, a(m^2 +m) = m+1, a(k) = m if m^2 +m+1 <= k <= m^2 +2m.

Example

The largest value among terms a(0) through a(14) is 4. So a(15) = floor(15/4) = 3.

Mathematica

a = {1}; Do[AppendTo[a, Floor[n/Max@ a]], {n, 2, 120}]; {1}~Join~a (* Michael De Vlieger, Apr 25 2016 *)

Crossrefs

Cf. A103627, A137734.

Sequence in context: A240872 A328806 A326370 * A365576 A290983 A272887

Adjacent sequences: A137732 A137733 A137734 * A137736 A137737 A137738

Keyword

easy,nonn

Author

Leroy Quet, Feb 09 2008

Status

approved