cp's OEIS Frontend

A235801 Length of n-th horizontal line segment in a diagram of a two-dimensional version of the 3x+1 (or Collatz) problem.

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