A255056 Trunk of number-of-runs beanstalk: The unique infinite sequence such that a(n-1) = a(n) - number of runs in binary representation of a(n).

0, 2, 4, 6, 10, 12, 14, 18, 22, 26, 28, 30, 32, 36, 42, 46, 50, 54, 58, 60, 62, 64, 68, 74, 78, 84, 90, 94, 96, 100, 106, 110, 114, 118, 122, 124, 126, 128, 132, 138, 142, 148, 152, 156, 162, 168, 174, 180, 186, 190, 192, 196, 202, 206, 212, 218, 222, 224, 228, 234, 238, 242, 246, 250, 252, 254

Offset: 0

Author

Antti Karttunen, Feb 14 2015

Keywords

• nonn
• base

Comments

All numbers of the form (2^n)-2 are present, which guarantees the uniqueness and also provides a well-defined method to compute the sequence, for example, via a partially reversed version A255066.

The sequence was inspired by a similar "binary weight beanstalk", A179016, sharing some general properties with it (like its partly self-copying behavior, see A255071), but also differing in some aspects. For example, here the branching degree is not the constant 2, but can vary from 1 to 4. (Cf. A255058.)

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16142

Crossrefs

First differences: A255336.

Terms halved: A255057.

Cf. A255053 & A255055 (the lower & upper bound for a(n)) and also A255123, A255124 (distances to those limits).

Cf. A255327, A255058 (branching degree for node n), A255330 (number of nodes in the finite subtrees branching from the node n), A255331, A255332

Subsequence: A000918 (except for -1).

Cf. A255061, A255062, A255071, A255072, A255066, A255122.

Cf. A254113, A254114.

Cf. A255063, A255064, A255125, A255126.

Similar "beanstalk's trunk" sequences using some other subtracting map than A236840: A179016, A219648, A219666.

Programs

Scheme

(define (A255056 n) (A255066 (A255122 n)))

Formula

a(n) = A255066(A255122(n)).

Other identities and observations. For all n >= 0:

a(n) = 2*A255057(n).

A255072(a(n)) = n.

A255053(n) <= a(n) <= A255055(n).