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A292595 a(n) = A000120(A292591(n)).

%I A292595 #10 Sep 23 2017 19:14:56
%S A292595 0,1,1,2,1,2,3,1,3,4,2,4,2,1,4,5,2,1,6,3,6,7,1,7,3,3,7,3,4,7,8,2,2,9,
%T A292595 4,9,10,2,1,11,1,11,4,4,11,4,5,3,12,2,12,13,1,13,14,6,14,5,3,2,4,6,1,
%U A292595 15,7,15,5,1,15,16,7,1,5,3,16,17,3,4,18,7,3,19,3,19,5,4,19,2,7,19,20,8,5,5,2,20,21,2,21,22,9,5,7,4,2
%N A292595 a(n) = A000120(A292591(n)).
%C A292595 If n > 1, then locate the node which contains n in binary tree A245612 (or in its mirror-image A244154) and traverse from that node towards the root [by iterating the map n -> A285712(n)], at the same time counting all numbers of the form 3k+1 that occur on the path, down to the final 1. This count includes also n itself if it is of the form 3k+1, with k > 0 (thus a(1) = 0).
%H A292595 Antti Karttunen, <a href="/A292595/b292595.txt">Table of n, a(n) for n = 1..8505</a>
%H A292595 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A292595 a(1) = 0, a(2) = 1, and for n > 1, a(n) = a(A285712(n)) + [1 == (n mod 3)].
%F A292595 a(n) = A000120(A292591(n)).
%F A292595 a(n) + A292594(n) = A285715(n).
%o A292595 (Scheme) (define (A292595 n) (if (<= n 2) (- n 1) (+ (if (= 1 (modulo n 3)) 1 0) (A292595 (A285712 n)))))
%Y A292595 Cf. A000120, A285712, A285715, A292591, A292594.
%K A292595 nonn
%O A292595 1,4
%A A292595 _Antti Karttunen_, Sep 20 2017