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

1,2

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

.                                | 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 .

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 *)

Prog

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

Crossrefs

Sequence in context: A159685 A370804 A251729 * A187262 A117670 A368253

Adjacent sequences: A187760 A187761 A187762 * A187764 A187765 A187766

Keyword

nonn

Author

Reinhard Zumkeller, Jan 04 2013

Status

approved