Search: id:A063694
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%I A063694
%S A063694 0,1,0,1,4,5,4,5,0,1,0,1,4,5,4,5,16,17,16,17,20,21,20,21,16,17,16,17,
%T A063694 20,21,20,21,0,1,0,1,4,5,4,5,0,1,0,1,4,5,4,5,16,17,16,17,20,21,20,21,
%U A063694 16,17,16,17,20,21,20,21,64,65,64,65,68,69,68,69,64,65,64,65,68,69,68
%N A063694 Remove odd-positioned bits from the binary expansion of n.
%H A063694 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A063694 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A063694 a(n) = sum( k>=0, (-1)^k*2^k*floor(n/2^k) )
%F A063694 a(n) = n-2*a(floor(n/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 
               23 2003
%F A063694 G.f. 1/(1-x) * sum(k>=0, (-2)^k*x^2^k/(1-x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               May 05 2003
%e A063694 E.g. a(25) = 17 because 25 = 11001 in binary and when we AND this with 
               10101 we are left with 10001 = 17.
%p A063694 [seq(every_other_pos(j,2,0),j=0..120)]; every_other_pos := proc(nn,x,
               w) local n,i,s; n := nn; i := 0; s := 0; while(n > 0) do if((i mod 
               2) = w) then s := s + ((x^i)*(n mod x)); fi; n := floor(n/x); i := 
               i+1; od; RETURN(s); end;
%o A063694 (PARI) /since n> ceil(log(n)/log(2)) / a(n)=sum(k=0,n,(-1)^k*2^k*floor(n/
               2^k))
%o A063694 (PARI) /since n> ceil(log(n)/log(2)) / a(n)=if(n<0,0,sum(k=0,n,(-1)^k*2^k*floor(n/
               2^k)))
%Y A063694 A001477[n] = a[n]+A063695[n]
%Y A063694 Sequence in context: A031349 A036444 A125583 this_sequence A068901 A010710 
               A021026
%Y A063694 Adjacent sequences: A063691 A063692 A063693 this_sequence A063695 A063696 
               A063697
%K A063694 nonn
%O A063694 0,5
%A A063694 Antti Karttunen Aug 03 2001

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