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A292596 a(1) = a(2) = 0; for n > 2, a(n) = A010051(n) + 2*a(floor(n/2)).

%I A292596 #9 Sep 27 2017 21:21:26
%S A292596 0,0,1,0,1,2,3,0,0,2,3,4,5,6,6,0,1,0,1,4,4,6,7,8,8,10,10,12,13,12,13,
%T A292596 0,0,2,2,0,1,2,2,8,9,8,9,12,12,14,15,16,16,16,16,20,21,20,20,24,24,26,
%U A292596 27,24,25,26,26,0,0,0,1,4,4,4,5,0,1,2,2,4,4,4,5,16,16,18,19,16,16,18,18,24,25,24,24,28,28,30,30,32,33,32,32,32,33
%N A292596 a(1) = a(2) = 0; for n > 2, a(n) = A010051(n) + 2*a(floor(n/2)).
%C A292596 1-bits in base-2 expansion of a(n) indicate the positions of odd primes in the sequence [n, floor(n/2), floor(n/4), ..., 1].
%H A292596 Antti Karttunen, <a href="/A292596/b292596.txt">Table of n, a(n) for n = 1..16384</a>
%H A292596 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A292596 a(1) = a(2) = 0; for n > 2, a(n) = A010051(n) + 2*a(floor(n/2)).
%F A292596 Other identities. For all n >= 1:
%F A292596 a(n) + A292597(n) = n.
%F A292596 A000120(a(n)) = A292598(n).
%F A292596 A007814(1+a(n)) <= A007814(1+n).
%o A292596 (Scheme, with memoization-macro definec)
%o A292596 (definec (A292596 n) (if (<= n 2) 0 (+ (A010051 n) (* 2 (A292596 (floor->exact (/ n 2)))))))
%Y A292596 Cf. A010051, A292597, A292598.
%Y A292596 Cf. also A292599 (variant for all primes).
%K A292596 nonn
%O A292596 1,6
%A A292596 _Antti Karttunen_, Sep 27 2017