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Search: id:A063694
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| A063694 |
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Remove odd-positioned bits from the binary expansion of n. |
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+0
7
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| 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, 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, 16, 17, 16, 17, 20, 21, 20, 21, 64, 65, 64, 65, 68, 69, 68, 69, 64, 65, 64, 65, 68, 69, 68
(list; graph; listen)
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OFFSET
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0,5
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(n) = sum( k>=0, (-1)^k*2^k*floor(n/2^k) )
a(n) = n-2*a(floor(n/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 23 2003
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
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EXAMPLE
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E.g. a(25) = 17 because 25 = 11001 in binary and when we AND this with 10101 we are left with 10001 = 17.
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MAPLE
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[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;
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PROGRAM
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(PARI) /since n> ceil(log(n)/log(2)) / a(n)=sum(k=0, n, (-1)^k*2^k*floor(n/2^k))
(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)))
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CROSSREFS
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A001477[n] = a[n]+A063695[n]
Sequence in context: A031349 A036444 A125583 this_sequence A068901 A010710 A021026
Adjacent sequences: A063691 A063692 A063693 this_sequence A063695 A063696 A063697
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Aug 03 2001
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