A213186 For the Collatz (3x+1) iteration starting at n, number of integers k such that T(n,k) = T(n-1,k) where T(n,k) is the k-th number of the trajectory.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 0, 0, 0, 16, 0, 5, 0, 9, 0, 0, 0, 0, 0, 16, 9, 0, 0, 0, 0, 9, 0, 19, 16, 0, 0, 0, 0, 0, 0, 14, 9, 0, 0, 0, 16, 20, 0, 9, 0, 106, 0, 0, 0, 0, 0, 17, 0, 95, 0, 0, 16, 23, 0, 12, 9, 0, 0, 0, 0, 0, 0, 20, 0, 27, 0, 0, 0

Offset

1,13

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

a(13) = 7 because the Collatz iterations starting at 13 and 12 are :
T(13,k) =[13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
T(12,k) =[12, 6, 3, 10, 5, 16, 8,  4, 2, 1]  and the 7 common values with the same indices are :
T(13,4) = T(12,4) = 10 ;
T(13,5) = T(12,5) = 5 ;
T(13,6) = T(12,6) = 16 ;
T(13,7) = T(12,7) = 8 ;
T(13,8) = T(12,8) = 4 ;
T(13,9) = T(12,9) = 2 ;
T(13,10) = T(12,10) = 1.

Maple

nn:=200:T:=array(1..nn):U:=array(1..nn): aa:=1:
for i from 1 to nn do:
   U[i]:=0:
od:
      for n from 1 to nn do:
          a:=0:k:=0:x:=n:
               for i from 1 to 10^8 while (x>1) do:
                  if irem(x, 2)=0 then
                  x := x/2:a:=a+1:k:=k+1:T[k]:=x:
              else
                 x := 3*x+1: a := a+1: k:=k+1:T[k]:=x:
               fi:
            od:
           it:=0:
                for j from 1 to min(a, aa) do:
                   if T[j]=U[j] then
                   it:=it+1:
                 else
                 fi:
                od:
                     for m from 1 to a do:
                        U[m]:=T[m]:
                     od:
          aa:=a: printf(`%d, `, it):
      od:

Crossrefs

Cf. A006577, A213185.

Sequence in context: A283881 A178308 A320377 * A296482 A272429 A308157

Adjacent sequences: A213183 A213184 A213185 * A213187 A213188 A213189

Keyword

nonn

Author

Michel Lagneau, Feb 28 2013

Status

approved