A139124 Starting from 1, at any step count the appearances of k, where k ranges from the highest number to 1.

1, 1, 2, 1, 2, 2, 3, 1, 3, 3, 3, 3, 4, 1, 5, 3, 4, 1, 2, 6, 3, 5, 1, 2, 2, 7, 4, 6, 1, 2, 2, 3, 7, 6, 7, 3, 3, 2, 3, 8, 8, 8, 3, 3, 3, 2, 3, 11, 9, 8, 1, 0, 1, 4, 3, 3, 2, 3, 15, 10, 8, 1, 0, 0, 0, 1, 1, 1, 5, 3, 3, 2, 4, 18, 11, 10, 1, 0, 0, 1, 0, 0, 0, 2, 2, 1, 5, 3, 3, 3, 5, 20, 12, 14

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 15 2008

Keywords

• easy
• nonn

Examples

			Start from 1. There is just one 1. So the sequence becames 1,1. Then count two 1s.
So we have 1,1,2. Then one 2 and two 1 -> 1,1,2,1,2. Then two 2 and three 1 -> 1,1,2,1,2,2,3. Then one 3, three 2, three 1 -> 1,1,2,1,2,2,3,1,3,3. Then three 3, three 2 and four 1 -> 1,1,2,1,2,2,3,1,3,3,3,3,4. And so on.
		

Crossrefs

Cf. A030717, A333867.

Programs

Mathematica

s={1};Do[si={};Do[j=Max[s]-i+1;AppendTo[si,Count[s,j]],{i,Max[s]}];s=AppendTo[s,si]//Flatten,{n,15}];s (* James C. McMahon, Jun 29 2025 *)

Extensions

a(87)-a(89) inserted by James C. McMahon, Jun 29 2025