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Let f(0) = 1, f(1) = 12, f(2) = 223, f(3) = 3334, = f(4) = 44445, f(5) = 555556, etc. Sequence gives concatenation of 0, f(0), f(f(0)), f(f(f(0))), ...
4

%I #18 Dec 14 2022 16:25:55

%S 0,1,1,2,1,2,2,2,3,1,2,2,2,3,2,2,3,2,2,3,3,3,3,4,1,2,2,2,3,2,2,3,2,2,

%T 3,3,3,3,4,2,2,3,2,2,3,3,3,3,4,2,2,3,2,2,3,3,3,3,4,3,3,3,4,3,3,3,4,3,

%U 3,3,4,4,4,4,4,5,1,2,2,2,3,2,2,3,2,2,3,3,3,3

%N Let f(0) = 1, f(1) = 12, f(2) = 223, f(3) = 3334, = f(4) = 44445, f(5) = 555556, etc. Sequence gives concatenation of 0, f(0), f(f(0)), f(f(f(0))), ...

%e 0;

%e 1;

%e 1, 2;

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

%e 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 3, 4; ...

%e For large m, the m-th block is given by A085694.

%Y Cf. A085694, A000110, A048993 (the number of occurrences of k in n-th block).

%Y Row maxima of A120698.

%K nonn,base,easy

%O 0,4

%A _Philippe Deléham_, Aug 14 2003; revised Sep 18 2005

%E Edited by _Charles R Greathouse IV_, Apr 30 2010