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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 A308157 Adjacent sequences:  A213183 A213184 A213185 * A213187 A213188 A213189 KEYWORD nonn AUTHOR Michel Lagneau, Feb 28 2013 STATUS approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)