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 A213185 For the Collatz (3x+1) iteration starting at n, number of integers k such that T(n,k) = T(n-1,k) +1 where T(n,k) is the k-th number of the trajectory (n is not counted). 2
 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 3, 0, 0, 3, 1, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 3, 4, 0, 0, 2, 1, 2, 0, 1, 2, 0, 0, 1, 1, 1, 0, 2, 3, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 1, 1, 0, 4, 5, 0, 0, 3, 1, 1, 0, 1, 2, 0, 0, 1, 1, 1, 0, 2, 3, 0, 0, 5, 1, 0, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS T(n,k) is periodic, for example T(6,3) = 10 and T(7,3) = 11; T(10,3) = 16 and T(11,3) = 17, ………….. T(6+4m, 3) = 10 + 6m and T(6+4m+1, 3) = 10 + 6m+1. ................. LINKS Michel Lagneau, Table of n, a(n) for n = 1..10000 EXAMPLE a(7) = 2 because the Collatz iterations starting at 7 and 6 are : T(7,k) =[7, 22, 11, 34, 17, 52,  26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1] T(6,k) =[6, 3, 10, 5, 16, 8,  4, 2, 1] ; the number 7 is not counted => T(7,3) = T(6,3) + 1 and T(7,5) = T(6,5) + 1, hence a(7) = 2. 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]+1 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, A213186. Sequence in context: A025442 A260118 A128582 * A285716 A101606 A257469 Adjacent sequences:  A213182 A213183 A213184 * A213186 A213187 A213188 KEYWORD nonn AUTHOR Michel Lagneau, Feb 28 2013 STATUS approved

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)