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A187763 Number of common terms in consecutive Collatz trajectories.

%I A187763 #12 Jul 13 2013 12:03:48
%S A187763 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,
%T A187763 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,
%U A187763 20,9,17,20,95,5,5,16,23,14,12,9,15,9,9,9,5,5,20
%N A187763 Number of common terms in consecutive Collatz trajectories.
%C A187763 Size of intersection of row n and row n+1 in A070165.
%H A187763 Reinhard Zumkeller, <a href="/A187763/b187763.txt">Table of n, a(n) for n = 1..10000</a>
%H A187763 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A187763 .                                | Rows in A070165 (trajectories)
%e A187763 a(1) = #{1} = 1;                 | 1
%e A187763 a(2) = #{2,1} = 2;               | 2,1
%e A187763 a(3) = #{4,2,1} = 3;             | 3,10,5,16,8,4,2,1
%e A187763 a(4) = #{4,2,1} = 3;             | 4,2,1
%e A187763 a(5) = #{5,16,8,4,2,1} = 6;      | 5,16,8,4,2,1
%e A187763 a(6) = #{10,5,16,8,4,2,1} = 7;   | 6,3,10,5,16,8,4,2,1
%e A187763 a(7) = #{8,4,2,1} = 4;           | 7,22,11,34,17,52,26,13,40,20,10,5,..
%e A187763 a(8) = #{8,4,2,1} = 4;           | 8,4,2,1
%e A187763 a(9) = #{10,5,16,8,4,2,1} = 7;   | 9,28,14,7,22,11,34,17,52,26,13,40,..
%e A187763 a(10) = #{10,5,16,8,4,2,1} = 7;  | 10,5,16,8,4,2,1
%e A187763 a(11) = #{10,5,16,8,4,2,1} = 7;  | 11,34,17,52,26,13,40,20,10,5,16,8,4,..
%e A187763 a(12) = #{10,5,16,8,4,2,1} = 7.  | 12,6,3,10,5,16,8,4,2,1
%e A187763 .                                | 13,40,20,10,5,16,8,4,2,1 .
%t A187763 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 *)
%o A187763 (Haskell)
%o A187763 import Data.List (intersect)
%o A187763 a187763 n = a187763_list !! (n-1)
%o A187763 a187763_list = map length $
%o A187763                zipWith intersect a070165_tabf $ tail a070165_tabf
%K A187763 nonn
%O A187763 1,2
%A A187763 _Reinhard Zumkeller_, Jan 04 2013