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A341509 a(n) = 2^j if n is of the form 2^i - 2^j with i > j, and 0 otherwise.

%I A341509 #9 Feb 14 2021 18:40:19
%S A341509 0,1,2,1,4,0,2,1,8,0,0,0,4,0,2,1,16,0,0,0,0,0,0,0,8,0,0,0,4,0,2,1,32,
%T A341509 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,8,0,0,0,4,0,2,1,64,0,
%U A341509 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0
%N A341509 a(n) = 2^j if n is of the form 2^i - 2^j with i > j, and 0 otherwise.
%H A341509 Antti Karttunen, <a href="/A341509/b341509.txt">Table of n, a(n) for n = 0..65537</a>
%H A341509 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A341509 a(0) = 0, and for n >= 1, a(n) = A340375(n) * A006519(n).
%F A341509 a(n) = A156552(A014963(A005940(1+n))).
%o A341509 (PARI)
%o A341509 A006519(n) = (1<<valuation(n, 2));
%o A341509 A340375(n) = if(n<5, 1, n>>=valuation(n, 2); n++; n>>valuation(n, 2)==1); \\ After function "is" given in A023758
%o A341509 A341509(n) = if(!n,n,A340375(n)*A006519(n));
%Y A341509 Cf. A005940, A006519, A014963, A156552, A340375.
%Y A341509 Cf. A023758 (after its initial zero, gives the positions nonzero terms).
%K A341509 nonn
%O A341509 0,3
%A A341509 _Antti Karttunen_, Feb 13 2021