A187763 Number of common terms in consecutive Collatz trajectories.

1, 2, 3, 3, 6, 7, 4, 4, 7, 7, 7, 7, 10, 9, 5, 5, 13, 16, 8, 5, 5, 9, 7, 7, 11, 9, 9, 16, 9, 17, 5, 5, 14, 9, 9, 19, 16, 22, 9, 9, 5, 5, 16, 14, 9, 17, 7, 7, 16, 20, 12, 9, 12, 106, 9, 20, 16, 20, 9, 17, 20, 95, 5, 5, 16, 23, 14, 12, 9, 15, 9, 9, 9, 5, 5, 20

Offset: 1

Author

Reinhard Zumkeller, Jan 04 2013

Keywords

• nonn

Comments

Size of intersection of row n and row n+1 in A070165.

Examples

			.                                | Rows in A070165 (trajectories)
a(1) = #{1} = 1;                 | 1
a(2) = #{2,1} = 2;               | 2,1
a(3) = #{4,2,1} = 3;             | 3,10,5,16,8,4,2,1
a(4) = #{4,2,1} = 3;             | 4,2,1
a(5) = #{5,16,8,4,2,1} = 6;      | 5,16,8,4,2,1
a(6) = #{10,5,16,8,4,2,1} = 7;   | 6,3,10,5,16,8,4,2,1
a(7) = #{8,4,2,1} = 4;           | 7,22,11,34,17,52,26,13,40,20,10,5,..
a(8) = #{8,4,2,1} = 4;           | 8,4,2,1
a(9) = #{10,5,16,8,4,2,1} = 7;   | 9,28,14,7,22,11,34,17,52,26,13,40,..
a(10) = #{10,5,16,8,4,2,1} = 7;  | 10,5,16,8,4,2,1
a(11) = #{10,5,16,8,4,2,1} = 7;  | 11,34,17,52,26,13,40,20,10,5,16,8,4,..
a(12) = #{10,5,16,8,4,2,1} = 7.  | 12,6,3,10,5,16,8,4,2,1
.                                | 13,40,20,10,5,16,8,4,2,1 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Programs

Haskell

import Data.List (intersect)
a187763 n = a187763_list !! (n-1)
a187763_list = map length $
               zipWith intersect a070165_tabf $ tail a070165_tabf

Mathematica

coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; Table[Length[Intersection[coll[n],coll[n+1]]],{n,76}] (* Jayanta Basu, May 28 2013 *)