%N 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).
%C 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.
%C 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.)
%H Antti Karttunen, <a href="/A255056/b255056.txt">Table of n, a(n) for n = 0..16142</a>
%F a(n) = A255066(A255122(n)).
%F Other identities and observations. For all n >= 0:
%F a(n) = 2*A255057(n).
%F A255072(a(n)) = n.
%F A255053(n) <= a(n) <= A255055(n).
%o (Scheme) (define (A255056 n) (A255066 (A255122 n)))
%Y First differences: A255336.
%Y Terms halved: A255057.
%Y Cf. A255053 & A255055 (the lower & upper bound for a(n)) and also A255123, A255124 (distances to those limits).
%Y Cf. A255327, A255058 (branching degree for node n), A255330 (number of nodes in the finite subtrees branching from the node n), A255331, A255332
%Y Subsequence: A000918 (except for -1).
%Y Cf. A255061, A255062, A255071, A255072, A255066, A255122.
%Y Cf. A254113, A254114.
%Y Cf. A255063, A255064, A255125, A255126.
%Y Similar "beanstalk's trunk" sequences using some other subtracting map than A236840: A179016, A219648, A219666.
%A _Antti Karttunen_, Feb 14 2015