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A056973 Number of blocks of {0,0} in the binary expansion of n. 5
0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 4, 3, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 5, 4, 3, 3, 3, 2, 2, 2, 3, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 4, 3, 2, 2, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

R. Stephan, Table of generating functions

Eric Weisstein's World of Mathematics, Digit Block.

Index entries for sequences related to binary expansion of n

FORMULA

a(2n) = a(n) + [n is even], a(2n+1) = a(n).

G.f.: 1/(1-x) * Sum_{k>=0} t^4/((1+t)*(1+t^2)) where t=x^(2^k). - Ralf Stephan, Sep 10 2003

a(n) = A023416(n) - A033264(n). - Ralf Stephan, Sep 10 2003

MAPLE

f:= proc(n) option remember;

     if n mod 4 = 0 then 1 + procname(n/2)

     else procname(floor(n/2))

     fi

end proc:

f(1):= 0:

map(f, [$1..200]); # Robert Israel, Sep 02 2015

MATHEMATICA

f[n_] := Count[Partition[IntegerDigits[n, 2], 2, 1], {0, 0}]; Table[f@ n, {n, 0, 102}] (* Michael De Vlieger, Sep 01 2015, after Robert G. Wilson v at A014081 *)

SequenceCount[#, {0, 0}, Overlaps->True]&/@(IntegerDigits[#, 2]&/@Range[0, 120]) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 24 2018 *)

PROG

(Haskell)

a056973 = f 0 where

   f y x = if x == 0 then y else f (y + 0 ^ (mod x 4)) $ div x 2

-- Reinhard Zumkeller, Mar 31 2015

(PARI)

a(n) = { my(x = bitor(n, n>>1));

         if (x == 0, 0, 1 + logint(x, 2) - hammingweight(x)) }

vector(102, i, a(i))  \\ Gheorghe Coserea, Sep 01 2015

CROSSREFS

Cf. A003754, A014081, A023416, A033264, A037800.

Cf. A107782.

Sequence in context: A046660 A183094 A108730 * A107782 A086017 A000161

Adjacent sequences:  A056970 A056971 A056972 * A056974 A056975 A056976

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified August 18 22:17 EDT 2018. Contains 313840 sequences. (Running on oeis4.)