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A063694 Remove odd-positioned bits from the binary expansion of n. 7
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; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(n) = Sum_{k>=0} (-1)^k*2^k*floor(n/2^k).

a(n) = n-2*a(floor(n/2)). - Vladeta Jovovic, Feb 23 2003

G.f. 1/(1-x) * sum(k>=0, (-2)^k*x^2^k/(1-x^2^k)). - Ralf Stephan, May 05 2003

a(n) = 4*a(floor(n/4)) + (n mod 4) mod 2. - Reinhard Zumkeller, Sep 26 2015

EXAMPLE

E.g. a(25) = 17 because 25 = 11001 in binary and when we AND this with 10101 we are left with 10001 = 17.

MAPLE

[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;

MATHEMATICA

a[n_] := BitAnd[n, Sum[2^k, {k, 0, Log[2, n] // Floor, 2}]]; Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Feb 28 2016 *)

PROG

(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)))

(Haskell)

a063694 0 = 0

a063694 n = 4 * a063694 n' + mod q 2

            where (n', q) = divMod n 4

-- Reinhard Zumkeller, Sep 26 2015

CROSSREFS

A001477[n] = a[n]+A063695[n]

Sequence in context: A036444 A125583 A196619 * A242624 A068901 A010710

Adjacent sequences:  A063691 A063692 A063693 * A063695 A063696 A063697

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 03 2001

STATUS

approved

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Last modified October 23 18:52 EDT 2018. Contains 316530 sequences. (Running on oeis4.)