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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 limiting value of f(0), f(f(0)), f(f(f(0))), ...
1

%I #11 Dec 14 2022 16:26:01

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

%T 4,3,3,3,4,3,3,3,4,3,3,3,4,4,4,4,4,5,2,2,3,2,2,3,3,3,3,4,2,2,3,2,2,3,

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

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

%C The positions where 1, 2, 3, 4, 5, ... appear are 1, 2, 5, 15, 52, ... (Bell numbers A000110).

%Y Cf. A085693, A000110, A048993 (the number of occurrences of k in n-th block).

%K nonn,easy

%O 1,2

%A _Philippe Deléham_, Aug 14 2003

%E Extended by _Philippe Deléham_, Jun 10 2005