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

Author

Clark Kimberling

Keywords

• nonn

Examples

			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;
		

Links

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

Crossrefs

Cf. A030717 (1st list).

Programs

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 *)

Extensions

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