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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). 33

%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 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.

%K nonn,base

%O 0,2

%A _Antti Karttunen_, Feb 14 2015

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)