login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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