A030718 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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

Offset

1,4

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Example

Second list begins:
  1;
  1;
  1, 2;
  1, 2;
  1, 2, 3;
  1, 2, 3;
  1, 2, 3, 4;
  1, 2, 3, 4, 5;
  1, 2, 3, 4, 5, 6;
  1, 2, 3, 4, 5, 6, 7;
  1, 2, 3, 4, 5, 6, 7;
  1, 2, 3, 4, 5, 6, 7, 8;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 11;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20;

Mathematica

s = t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]]; AppendTo[s, Union@ Flatten@ t], {12}]; Flatten[s] (* Michael De Vlieger, Nov 15 2022, after Peter J. C. Moses at A030717 *)

Crossrefs

Cf. A030717 (1st list).

Sequence in context: A249727 A023118 A122197 * A227779 A194066 A308916

Adjacent sequences: A030715 A030716 A030717 * A030719 A030720 A030721

Keyword

nonn

Author

Clark Kimberling

Extensions

Name revised in line with A030778 by Peter Munn, Oct 11 2022

Status

approved