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

1,3

Comments

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

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

Example

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;
  ...

Crossrefs

Cf. A365838, A306211.

Sequence in context: A160735 A216338 A227725 * A331244 A316845 A120481

Adjacent sequences: A365833 A365834 A365835 * A365837 A365838 A365839

Keyword

nonn,tabf

Author

Neal Gersh Tolunsky, Sep 19 2023

Status

approved