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

0,3

Links

Table of n, a(n) for n=0..93.

Example

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.

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 *)

Crossrefs

Cf. A030717, A333867.

Sequence in context: A249337 A316848 A380968 * A024160 A295283 A103284

Adjacent sequences: A139121 A139122 A139123 * A139125 A139126 A139127

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 15 2008

Extensions

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

Status

approved