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%I #10 May 19 2020 14:36:32
%S 1,1,2,2,2,2,3,2,3,2,3,3,3,3,4,3,3,3,4,3,3,3,4,3,4,3,4,4,4,4,5,3,4,3,
%T 4,4,4,4,5,3,4,3,4,4,4,4,5,4,4,4,5,4,4,4,5,4,5,4,5,5,5,5,6,4,4,4,5,4,
%U 4,4,5,4,5,4,5,5,5,5,6,4,4,4,5,4,4,4,5,4,5,4
%N Number of applications of f to reduce n to 1, where f(k) is the integer among k/2,(k+1)/4, (k+3)/4.
%C Alternatively, a(n+1) is the number of periods of the prefix of length n of the period-doubling word (A035263). - _Jeffrey Shallit_, May 19 2020
%C Alternatively, a(n+1) is the length of the (unique factorization) of the base-2 representation of n into the blocks 1, 00, and 10. - _Jeffrey Shallit_, May 19 2020
%e a(11)=3, which counts these reductions: 11->4->2->1.
%Y Cf. A035263.
%K nonn
%O 2,3
%A _Clark Kimberling_, Sep 03 2000