cp's OEIS Frontend

A277007 Number of maximal runs of 1-bits (in binary expansion of n) such that the length of run > 1 + the total number of zeros anywhere right of that run.

%I A277007 #13 Sep 26 2016 20:42:36
%S A277007 0,0,0,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,
%T A277007 0,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,2,1,1,1,1,0,0,0,1,
%U A277007 0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,2,0
%N A277007 Number of maximal runs of 1-bits (in binary expansion of n) such that the length of run > 1 + the total number of zeros anywhere right of that run.
%H A277007 Antti Karttunen, <a href="/A277007/b277007.txt">Table of n, a(n) for n = 0..8191</a>
%H A277007 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A277007 a(n) = A276077(A005940(1+n)).
%e A277007 For n=3, "11" in binary, the only maximal run of 1-bits is of length 2, and 2 > 0+1 (where 0 is the total number of zeros to the right of it), thus a(3) = 1.
%e A277007 For n=59, "111011" in binary, both the length of run "11" at the least significant end exceeds the limit (see case n=3 above), and also the length of run "111" exceeds 1 + the total number of 0's to the right of it, thus a(59) = 1+1 = 2.
%e A277007 For n=60, "111100" in binary, the length of only run of 1's is 4, and 4 > 2+1, thus a(60) = 1.
%e A277007 For n=118, "1110110" in binary, the length of rightmost run of 1-bits is 2, but that is not > 1+1 (one more than the number of 0-bits right to it). Also, the length of the leftmost run of 1-bits is 3, but that is not > 1+2, thus a(118) = 0.
%e A277007 For n=246, "11110110" in binary, the rightmost run of 1-bits does not contribute, but the leftmost run of 1-bits has now length 4, which is more than 1+2 (where 2 is the total number of 0-bits right of it), thus a(246) = 1.
%o A277007 (Scheme)
%o A277007 ;; Standalone iterative implementation:
%o A277007 (define (A277007 n) (let loop ((e 0) (n n) (z 0) (r 0)) (cond ((zero? n) (+ e (if (> r (+ 1 z)) 1 0))) ((even? n) (loop (+ e (if (> r (+ 1 z)) 1 0)) (/ n 2) (+ 1 z) 0)) (else (loop e (/ (- n 1) 2) z (+ 1 r))))))
%Y A277007 Cf. A277008 (positions of zeros), A277009 (of nonzeros).
%Y A277007 Cf. A005940, A277011, A277012, A276077.
%Y A277007 Differs from the similar entry A277017 for the first time at n=60, where a(60)=1, while A277017(60)=0.
%K A277007 nonn,base
%O A277007 0,60
%A A277007 _Antti Karttunen_, Sep 25 2016