A365836 a(1)=1; thereafter extend the sequence by appending its nonincreasing run transform, recompute the nonincreasing run transform, append it, and so on.

1, 1, 2, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 2, 3, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 1, 2, 3, 1, 2, 1, 2, 2

Offset: 1

Author

Neal Gersh Tolunsky, Sep 19 2023

Keywords

• nonn
• tabf

Comments

The nonincreasing run transform replaces each run of weakly decreasing terms with a single value which is the length of that run.

Examples

			Irregular triangle in which each row (after the initial 1) is the nonincreasing run transform of the concatenation of the previous rows:
  1;
  1;
  2;
  2, 1;
  2, 3;
  2, 3, 1, 1;
  2, 3, 1, 2, 3;
  2, 3, 1, 2, 3, 1, 2, 1, 1;
  2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3;
  2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 2, 3, 1, 1;
  ...
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10632 (first 25 rows)
• Neal Gersh Tolunsky, Ordinal transform on the first 35 iterations of the sequence

Crossrefs

Cf. A365838, A306211.