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a(1)=1; thereafter extend the sequence by appending its nonincreasing run transform, recompute the nonincreasing run transform, append it, and so on.
2

%I #24 Sep 26 2023 13:38:47

%S 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,

%T 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,

%U 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

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

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

%H Neal Gersh Tolunsky, <a href="/A365836/b365836.txt">Table of n, a(n) for n = 1..10632</a> (first 25 rows)

%H Neal Gersh Tolunsky, <a href="/A365836/a365836.png">Ordinal transform on the first 35 iterations of the sequence</a>

%e Irregular triangle in which each row (after the initial 1) is the nonincreasing run transform of the concatenation of the previous rows:

%e 1;

%e 1;

%e 2;

%e 2, 1;

%e 2, 3;

%e 2, 3, 1, 1;

%e 2, 3, 1, 2, 3;

%e 2, 3, 1, 2, 3, 1, 2, 1, 1;

%e 2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3;

%e 2, 3, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 2, 3, 1, 1;

%e ...

%Y Cf. A365838, A306211.

%K nonn,tabf

%O 1,3

%A _Neal Gersh Tolunsky_, Sep 19 2023