A218549 -id:A218549 - cp's OEIS frontend

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

Antti Karttunen, Nov 01 2012

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).

			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.

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

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.

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

A218548 Positions of records in A213726.

Original entry on oeis.org

0, 2, 10, 22, 47, 208, 224, 974, 1934, 1972, 3765, 3893, 8058, 15738, 16122, 65080, 129592, 130104

Offset: 1

Antti Karttunen, Nov 04 2012

			See explanation at A218549.

Cf. A213726, A218549, A218550. All terms are found from A213730.

A218613 Sizes of distinct new sidetrees ("tendrils", in the order of their appearance) that sprout along (A218787) the infinite trunk of beanstalk (A179016).

Original entry on oeis.org

0, 1, 2, 3, 2, 5, 6, 4, 4, 5, 5, 9, 10, 17, 17, 5, 19, 32, 6, 10, 8, 4, 3, 10, 33, 4, 5, 7, 34, 20, 31, 5, 62, 4, 7, 4, 5, 14, 33, 7, 54, 32, 12, 14, 3, 34, 47, 4, 8, 31, 32, 143, 10, 11, 17, 169, 13, 240, 59, 8, 7, 15, 18, 12, 33, 102, 5, 66, 116, 6, 11, 15

Offset: 1

Antti Karttunen, Nov 11 2012

nonn

a(n) = A213726(A218612(n))-1. All values A218549(n)-1 occur here at some point and in order.

(define (A218613 n) (A218786 (A218611 n)))

a(n) = A218786(A218611(n)).

A218550 a(n) = A213725(A218548(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 19, 15, 16, 27, 39, 51, 67

Offset: 1

Antti Karttunen, Nov 04 2012

a(n) tells the maximum depth + 1 of the n-th record size finite side-tree in the infinite beanstalk.

			a(7)=6 as the finite tree of 7 leaves (233, 234, 235, 238, 245, 250 and 251) and 6 internal vertices (244, 239, 232, 229, 228 and 224) rooted at 224 has the maximum depth of 5 (the path 224 -> 228 -> 232 -> 239 -> 244 -> 250/251).

Cf. A218549.

(define (A218550 n) (A213725 (A218548 n)))

cp's OEIS Frontend

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.

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A218548 Positions of records in A213726.

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A218613 Sizes of distinct new sidetrees ("tendrils", in the order of their appearance) that sprout along (A218787) the infinite trunk of beanstalk (A179016).

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A218550 a(n) = A213725(A218548(n)).

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