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A292597 a(1) = 1; for n > 1, a(n) = c(n) + 2*a(floor(n/2)), where c(n) is the characteristic function of odd composites, A071904.

%I A292597 #6 Sep 27 2017 21:21:34
%S A292597 1,2,2,4,4,4,4,8,9,8,8,8,8,8,9,16,16,18,18,16,17,16,16,16,17,16,17,16,
%T A292597 16,18,18,32,33,32,33,36,36,36,37,32,32,34,34,32,33,32,32,32,33,34,35,
%U A292597 32,32,34,35,32,33,32,32,36,36,36,37,64,65,66,66,64,65,66,66,72,72,72,73,72,73,74,74,64,65,64,64,68,69,68,69,64,64,66,67
%N A292597 a(1) = 1; for n > 1, a(n) = c(n) + 2*a(floor(n/2)), where c(n) is the characteristic function of odd composites, A071904.
%C A292597 1-bits in base-2 expansion of a(n) indicate the positions of odd nonprimes in the sequence [n, floor(n/2), floor(n/4), ..., 1].
%H A292597 Antti Karttunen, <a href="/A292597/b292597.txt">Table of n, a(n) for n = 1..16384</a>
%H A292597 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A292597 a(1) = 1; for n > 1, a(n) = (A000035(n)*(1-A010051(n))) + 2*a(floor(n/2)).
%F A292597 For all n >= 1, a(n) + A292596(n) = n.
%o A292597 (Scheme, with memoization-macro definec)
%o A292597 (definec (A292597 n) (if (= 1 n) 1 (+ (* (A000035 n) (- 1 (A010051 n))) (* 2 (A292597 (floor->exact (/ n 2)))))))
%Y A292597 Cf. A000035, A010051, A014076, A071904, A292596, A292598.
%K A292597 nonn
%O A292597 1,2
%A A292597 _Antti Karttunen_, Sep 27 2017