OFFSET

0,8

COMMENTS

Both the 3x+1 steps and the halving steps are counted. The asymptotic growth rate appears to be the same as A005186, about 1.26 (A176014).

a(n) is, for n >= 4, the number of 4 (mod 6) nodes (vertices) of row n-1 of the Collatz tree A127824. The node 4 has in A127824 outdegree 1 in order to avoid a repetition of the whole tree. - Wolfdieter Lang, Mar 26 2014

The heuristic arguments given in the LINKS of A005186 suggest that this sequence has the same asymptotic growth rate (3+sqrt(21))/6. - Markus Sigg, Sep 07 2024

LINKS

Markus Sigg, Table of n, a(n) for n = 0..125 (first 71 terms from T. D. Noe).

Wolfdieter Lang, On Collatz' Words, Sequences and Trees, arXiv preprint arXiv:1404.2710, 2014 and J. Int. Seq. 17 (2014) # 14.11.7.

EXAMPLE

23, 141, 151, 853, 909, and 5461 are the only odd numbers that require exactly 15 iterations to reach 1. Hence a(15)=6.

At row 15 with a(16) = 5 nodes 4 (mod 6) the left-right symmetry for the number of 4 (mod 6) nodes in the Collatz tree A127824 is broken for the first time: in the left half of the tree there are the three nodes 22, 136 and 832 but on the right half only the two nodes 904 and 5440. - Wolfdieter Lang, Mar 26 2014

CROSSREFS

KEYWORD

nonn

AUTHOR

T. D. Noe, Apr 27 2010

STATUS

approved