A277017 Number of maximal runs of 1-bits (in binary expansion of n) such that the length of run >= A000040(1 + the total number of zeros to the right of that run).

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, 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, 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, 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

Offset

0,60

Comments

a(n) = number of 1-runs in binary expansion of n that exceed the length allotted to that run by primorial base coding used in A277022. If a(n) = 0, then n is in the range of A277022.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Index entries for sequences related to primorial base

Formula

a(n) = A129251(A005940(1+n)).

Example

For n=3, "11" in binary, the only maximal run of 1-bits is of length 2, and 2 >= prime(0+1) (where 0 is the total number of zeros to the right of it), thus a(3) = 1.
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" >= prime(1 + the total number of 0's to the right of it) = prime(2) = 3, thus a(59) = 1+1 = 2.
For n=60, "111100" in binary, the length of only run of 1's is 4, and 4 < prime(2+1) = 5, thus a(60) = 0.

Prog

(Scheme)
(define (A277017 n) (let loop ((e 0) (n n) (z 0) (r 0)) (cond ((zero? n) (+ e (if (>= r (A000040 (+ 1 z))) 1 0))) ((even? n) (loop (+ e (if (>= r (A000040 (+ 1 z))) 1 0)) (/ n 2) (+ 1 z) 0)) (else (loop e (/ (- n 1) 2) z (+ 1 r))))))

Crossrefs

Cf. A277018 (positions of zeros), A277019 (of nonzeros).

Cf. A000040, A005940, A129251, A277021, A277022.

Differs from similar A277007 for the first time at n=60, where a(60)=0, while A277007(60)=1.

Sequence in context: A320655 A359786 A359763 * A178498 A353422 A095408

Adjacent sequences: A277014 A277015 A277016 * A277018 A277019 A277020

Keyword

nonn,base

Author

Antti Karttunen, Sep 26 2016

Status

approved