A255056 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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

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).

PROG

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

CROSSREFS

First differences: A255336.