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A292599 a(1) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)).

%I A292599 #13 Sep 29 2017 10:31:51
%S A292599 0,1,1,2,3,2,3,4,4,6,7,4,5,6,6,8,9,8,9,12,12,14,15,8,8,10,10,12,13,12,
%T A292599 13,16,16,18,18,16,17,18,18,24,25,24,25,28,28,30,31,16,16,16,16,20,21,
%U A292599 20,20,24,24,26,27,24,25,26,26,32,32,32,33,36,36,36,37,32,33,34,34,36,36,36,37,48,48,50,51,48,48,50,50,56,57,56,56,60,60,62,62,32
%N A292599 a(1) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)).
%C A292599 1-bits in base-2 expansion of a(n) indicate the positions of primes in the sequence [n, floor(n/2), floor(n/4), ..., 1].
%H A292599 Antti Karttunen, <a href="/A292599/b292599.txt">Table of n, a(n) for n = 1..16384</a>
%H A292599 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A292599 a(1) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)).
%F A292599 Other identities. For all n >= 1:
%F A292599 A000120(a(n)) = A078349(n).
%F A292599 A007814(1+a(n)) = A292936(n).
%p A292599 A292599 := proc(n)
%p A292599     option remember;
%p A292599     if n = 1 then
%p A292599         0 ;
%p A292599     else
%p A292599         A010051(n) + 2*procname(floor(n/2)) ;
%p A292599     end if;
%p A292599 end proc:
%p A292599 seq(A292599(n),n=1..100) ; # _R. J. Mathar_, Sep 28 2017
%t A292599 a[1] = 0; a[n_] := a[n] = Boole[PrimeQ[n]] + 2*a[Floor[n/2]]; Array[a, 96] (* _Jean-François Alcover_, Sep 29 2017 *)
%o A292599 (Scheme, with memoization-macro definec)
%o A292599 (definec (A292599 n) (if (<= n 1) 0 (+ (A010051 n) (* 2 (A292599 (floor->exact (/ n 2)))))))
%Y A292599 Cf. A010051, A078349, A292258, A292259, A292936.
%Y A292599 Cf. also A292596 (variant for odd primes).
%K A292599 nonn
%O A292599 1,4
%A A292599 _Antti Karttunen_, Sep 27 2017