%I
%S 0,2,4,6,10,12,14,18,22,26,28,30,32,36,42,46,50,54,58,60,62,64,68,74,
%T 78,84,90,94,96,100,106,110,114,118,122,124,126,128,132,138,142,148,
%U 152,156,162,168,174,180,186,190,192,196,202,206,212,218,222,224,228,234,238,242,246,250,252,254
%N Trunk of numberofruns beanstalk: The unique infinite sequence such that a(n1) = 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 welldefined 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 selfcopying 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.
%K nonn,base
%O 0,2
%A _Antti Karttunen_, Feb 14 2015
