%I #30 Jan 02 2022 00:32:36
%S 0,1,2,3,7,5,6,7,8,9,17,11,12,13,14,15,27,17,18,19,20,21,37,23,24,25,
%T 26,27,47,29,30,31,32,33,57,35,36,37,38,39,67,41,42,43,44,45,77,47,48,
%U 49,50,51,87,53,54,55,56,57,97,59,60,61,62,63,107,65,66
%N Length of n-th horizontal line segment in a diagram of a two-dimensional version of the 3x+1 (or Collatz) problem.
%C In the diagram every cycle is represented by a directed graph.
%C After (3x + 1) the next step is (3y + 1).
%C After (x/2) the next step is (y/2).
%C A235800(n) gives the length of n-th vertical line segment, from left to right, in the same diagram.
%H Chai Wah Wu, <a href="/A235801/b235801.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F a(n) = 10*k - 3, if n is of the form (6*k-2), k>=1, otherwise a(n) = n.
%F From _Chai Wah Wu_, Sep 26 2016: (Start)
%F a(n) = 2*a(n-6) - a(n-12) for n > 11.
%F G.f.: x*(x^2 + 1)*(x^3 + 2*x^2 + 1)*(x^5 + x^4 + 2*x + 1)/(x^12 - 2*x^6 + 1). (End)
%e The first part of the diagram in the first quadrant:
%e . . . . . . . . . . . . . . . . . . . . . . . .
%e . _ _|_ _|_ _|_ _|_ _|_ _|_ _|_ _.
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%e . | | | |_|_ _|_ _|_ _|_ _|_ _| . 11
%e . _ _|_ _|_ _|_ _ _|_ _|_ _|_ _|_ _| . 17
%e . | | | |_|_ _|_ _|_ _|_ _| . 9
%e . | | | _ _|_ _|_ _|_ _| . 8
%e . | | |_|_ _|_ _|_ _| . 7
%e . | | _ _|_ _|_ _| . 6
%e . | |_|_ _|_ _| . 5
%e . _ _|_ _ _|_ _| . 7
%e . | |_|_ _| . 3
%e . | _ _| . 2
%e . |_| . 1
%e . . . . . . . . . . . . . . . . . . . . . . . . 0
%e . a(n)
%e .
%e For an explanation of this diagram as the skeleton of a piping model see A235800. - _Omar E. Pol_, Dec 30 2021
%o (Python)
%o from __future__ import division
%o A235801_list = [n if n % 6 != 4 else 10*(n//6)+7 for n in range(10**4)] # _Chai Wah Wu_, Sep 26 2016
%Y Cf. A347270 (all 3x+1 sequences).
%Y Companion of A235800.
%Y Cf. A000027, A004767, A006370, A014682, A016957, A070165, A235795.
%K nonn
%O 0,3
%A _Omar E. Pol_, Jan 15 2014