A213726 a(n)=0 if n is in the infinite trunk of the "beanstalk" (i.e., in A179016), otherwise number of terminal nodes (leaves) in that finite branch of the beanstalk.

0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 3, 0, 1, 2, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 3, 0, 1, 2, 0, 1, 1, 1, 0, 4, 1, 0, 3, 1, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 3, 0, 1, 2, 0, 1, 1, 1, 0, 4, 1, 0, 3, 1, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 4, 1, 0, 3, 1, 1, 0, 2, 1, 0, 3, 1, 1, 1, 0, 2, 1, 0, 3, 1, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 3, 0, 1, 2, 0, 1, 1, 1, 0, 4, 1, 0, 3, 1, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 4, 1, 0, 3, 1, 1, 0, 2, 1, 0, 3, 1, 1, 1, 0, 2, 1, 0, 3, 1, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 1, 0, 4, 1, 0, 3, 1, 1, 0, 2, 1, 0, 3, 1, 1, 1, 0, 2, 1, 6

Offset

0,11

Comments

a(n) tells for each natural number n, whether it belongs to the infinite trunk of beanstalk (when a(n)=0), or if it is one of the terminal nodes (i.e., leaves, A055938) (when a(n)=1), or otherwise, when a(n)>1, tells from how many terminal nodes one can end to this n, by repeatedly subtracting their bit count (A000120) from them (as explained in A071542).

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Formula

If A079559(n)=0, a(n)=1; otherwise, if A213719(n)=1, a(n)=0; otherwise a(n) = a(A213723(n))+a(A213724(n)).

Example

a(10)=2 because the only numbers in A055938 from which one can end to 10 by the process described in A071542/A179016 are 12 and 13 (see comment at A213717). Similarly, a(22)=3 as there are following three cases: 24 as 24-A000120(24) = 24-2 = 22, and also 28 & 29 as 28-A000120(28) = 28-3 = 25, and 29-A000120(29) = 29-4 = 25, and then 25-A000120(25) = 25-3 = 22.

Prog

(Scheme with memoization-macro definec): (definec (A213726 n) (cond ((zero? (A079559 n)) 1) ((not (zero? (A213719 n))) 0) (else (+ (A213726 (A213723 n)) (A213726 (A213724 n))))))

Crossrefs

Differs from A213725 for the first time at n=208, where a(n)=6, while A213725(208)=5.

For all n, a(A179016(n)) = 0, a(A055938(n)) = 1, and a(A213717(n)) >= 2. For all n, A213727(A213717(n)) = (2*a(A213717(n)))-1. Cf. A213725-A213731. Records: A218548, A218549.

Sequence in context: A293139 A351319 A213725 * A116929 A059984 A046675

Adjacent sequences: A213723 A213724 A213725 * A213727 A213728 A213729

Keyword

nonn

Author

Antti Karttunen, Nov 01 2012

Status

approved