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 A235801 Length of n-th horizontal line segment in a diagram of a two-dimensional version of the Collatz (or 3x + 1) problem. 3
 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, 26, 27, 47, 29, 30, 31, 32, 33, 57, 35, 36, 37, 38, 39, 67, 41, 42, 43, 44, 45, 77, 47, 48, 49, 50, 51, 87, 53, 54, 55, 56, 57, 97, 59, 60, 61, 62, 63, 107, 65, 66 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS In the diagram every cycle is represented by a directed graph. After (3x + 1) the next step is (3y + 1). After (x/2) the next step is (y/2). A235800(n) gives the length of n-th vertical line segment, from left to right, in the same diagram. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 FORMULA a(n) = 10*k - 3, if n is of the form (6*k-2), k>=1, otherwise a(n) = n. From Chai Wah Wu, Sep 26 2016: (Start) a(n) = 2*a(n-6) - a(n-12) for n > 11. 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) EXAMPLE The first part of the diagram in the first quadrant: . . . . . . . . . . . . . . . . . . . . . . . . .              _ _|_ _|_ _|_ _|_ _|_ _|_ _|_ _. .             |   |   |   |   |   |   |   |_|_. .             |   |   |   |   |   |   |  _ _|_. .             |   |   |   |   |   |   |_|_ _|_. .             |   |   |   |   |   |  _ _|_ _|_. .             |   |   |   |   |   |_|_ _|_ _|_. .          _ _|_ _|_ _|_ _|_ _|_ _ _|_ _|_ _|_. .         |   |   |   |   |   |_|_ _|_ _|_ _|_. .         |   |   |   |   |  _ _|_ _|_ _|_ _|_. .         |   |   |   |   |_|_ _|_ _|_ _|_ _|_. .         |   |   |   |  _ _|_ _|_ _|_ _|_ _|_. .         |   |   |   |_|_ _|_ _|_ _|_ _|_ _| . 11 .      _ _|_ _|_ _|_ _ _|_ _|_ _|_ _|_ _|     . 17 .     |   |   |   |_|_ _|_ _|_ _|_ _|         .  9 .     |   |   |  _ _|_ _|_ _|_ _|             .  8 .     |   |   |_|_ _|_ _|_ _|                 .  7 .     |   |  _ _|_ _|_ _|                     .  6 .     |   |_|_ _|_ _|                         .  5 .  _ _|_ _ _|_ _|                             .  7 . |   |_|_ _|                                 .  3 . |  _ _|                                     .  2 . |_|                                         .  1 . . . . . . . . . . . . . . . . . . . . . . . .  0 .                                              a(n) PROG (Python) from __future__ import division A235801_list = [n if n % 6 != 4 else 10*(n//6)+7 for n in range(10**4)] # Chai Wah Wu, Sep 26 2016 CROSSREFS Cf. A000027, A004767, A006370, A014682, A016957, A070165, A235795, A235800. Sequence in context: A205299 A222242 A069771 * A076986 A225403 A069786 Adjacent sequences:  A235798 A235799 A235800 * A235802 A235803 A235804 KEYWORD nonn AUTHOR Omar E. Pol, Jan 15 2014 STATUS approved

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Last modified April 22 22:14 EDT 2019. Contains 322378 sequences. (Running on oeis4.)