A056974 Number of blocks of {0, 0, 0} in the binary expansion of n.
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 1, 0, 0, 0
Offset: 1
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
- Eric Weisstein's World of Mathematics, Digit Block
- Index entries for sequences related to binary expansion of n
Programs
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Mathematica
a[n_, bits_] := (idn = IntegerDigits[n, 2]; ln = Length[idn]; lb = Length[bits]; For[cnt = 0; k = 1, k <= ln - lb + 1, k++, If[idn[[k ;; k + lb - 1]] == bits, cnt++]]; cnt); Table[ a[n, {0, 0, 0}], {n, 1, 102} ] (* Jean-François Alcover, Oct 23 2012 *) Table[SequenceCount[IntegerDigits[n,2],{0,0,0},Overlaps->True],{n,110}] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Jan 10 2016 *) -
PARI
a(n)=my(v=binary(n));sum(i=3,#v,v[i]+v[i-1]+v[i-2]==0) \\ Charles R Greathouse IV, Dec 07 2011
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PARI
a(n) = { my(x = bitor(n, bitor(n>>1, n>>2))); if (x == 0, 0, 1 + logint(x, 2) - hammingweight(x)) }; vector(102, i, a(i)) \\ Gheorghe Coserea, Sep 17 2015 -
Scheme
;; This uses Ralf Stephan's recurrence and memoization-macro definec: (definec (A056974 n) (cond ((= 1 n) 0) ((even? n) (+ (if (zero? (modulo n 8)) 1 0) (A056974 (/ n 2)))) (else (A056974 (/ (- n 1) 2))))) ;; Antti Karttunen, Oct 10 2017
Formula
a(1) = 0, and then after, a(2n) = a(n) + [n congruent to 0 mod 8], a(2n+1) = a(n). - Ralf Stephan, Aug 22 2003, corrected by Antti Karttunen, Oct 10 2017
Comments