A079686 Start with 0; at n-th step, write down what is in the sequence so far.

0, 1, 0, 1, 1, 2, 0, 1, 2, 3, 1, 3, 0, 2, 3, 2, 2, 5, 1, 4, 0, 1, 5, 1, 4, 3, 3, 5, 2, 6, 1, 5, 0, 1, 6, 4, 5, 2, 4, 5, 3, 6, 2, 9, 1, 6, 0, 1, 9, 0, 8, 0, 7, 4, 6, 6, 5, 4, 4, 6, 3, 8, 2, 11, 1, 7, 0, 1, 11, 0, 10, 2, 9, 2, 8, 2

Offset: 0

Author

N. J. A. Sloane Jan 26 2003

Keywords

• nonn
• easy
• base

Comments

Start with the highest value currently in the sequence and count down to zero.

Examples

			After the sequence is "0, 1, 0, 1, 1, 2, 0", we see one "2", three "1"s, and three "0"s, so we add 1, 2, 3, 1, 3, 0 to the sequence.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005150. For other versions see A051120, A079668, A055186.

Programs

MATLAB

a=[0];c=2;d=2; for j=1:7 for k=max(a):-1:0 a(c)=size(find(a(1:d-1)==k),2); a(c+1)=k; c=c+2; end; d=c; end; a' % Nathaniel Johnston, Apr 25 2011

Mathematica

s={0}; Do[s=Flatten[{s, {Count[s,#],#}&/@Range[Max[s],0,-1]}], {60}]; s (* Peter J. C. Moses, Mar 21 2013 *)

Extensions

a(13) - a(75) from Nathaniel Johnston, Apr 25 2011