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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A198555

Adjacent sequences:  A213183 A213184 A213185 * A213187 A213188 A213189

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 28 2013

STATUS

approved

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Last modified April 19 09:13 EDT 2019. Contains 322241 sequences. (Running on oeis4.)