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%I #15 Sep 27 2018 17:54:53
%S 0,0,1,-1,2,-1,0,-1,3,-1,0,-1,1,-1,0,-1,4,-1,0,-1,1,-1,0,-1,2,-1,0,-1,
%T 1,-1,0,-1,5,-1,0,-1,1,-1,0,-1,2,-1,0,-1,1,-1,0,-1,3,-1,0,-1,1,-1,0,
%U -1,2,-1,0,-1,1,-1,0,-1,6,-1,0,-1,1,-1,0,-1,2,-1,0,-1,1,-1
%N First differences of A080791.
%C Number of trailing zeros in the binary representation of n, minus one if n is not a power of two.
%C a(0) = 0 by convention. - _Antti Karttunen_, Sep 27 2018
%H Antti Karttunen, <a href="/A089263/b089263.txt">Table of n, a(n) for n = 0..65537</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(0)=0, a(2n) = a(n) + 1, a(2n+1) = -1 + [n==0].
%F a(n) = A007814(n) + A036987(n-1) - 1.
%F G.f.: sum(k>=0, t^2/(1+t), t=x^2^k).
%F a(n) = A080791(n+1) - A080791(n). - _Antti Karttunen_, Sep 27 2018
%o (PARI) a(n)=if(!n,n,(valuation(n, 2)+(2^valuation(n, 2)==n)-1)); \\ Check for n=0 added by _Antti Karttunen_, Sep 27 2018
%o (PARI) a(n)=if(n<1,0,if(n%2==0,a(n/2)+1,-1+(((n-1)/2)==0)))
%Y Cf. A080791, A088705.
%K sign,easy
%O 0,5
%A _Ralf Stephan_, Oct 30 2003
%E Definition corrected (A023416 replaced with A080791) by _Antti Karttunen_, Sep 27 2018
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