

A255056


Trunk of numberofruns beanstalk: The unique infinite sequence such that a(n1) = a(n)  number of runs in binary representation of a(n).


33



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
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OFFSET

0,2


COMMENTS

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.
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.)


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.
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.
Sequence in context: A256773 A141104 A047410 * A164875 A301646 A024892
Adjacent sequences: A255053 A255054 A255055 * A255057 A255058 A255059


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Feb 14 2015


STATUS

approved



