A355569 - OEIS

%I #14 Oct 14 2022 08:54:53

%S 5,8,10,13,16,17,38,40,46,53,56,58,61,70,80,88,106,107,160,251,283,

%T 377,638,650,958,976,1367,1438,1822,2158,2429,2734,3238,4102,4616,

%U 4858,6154,7288,9232

%N Numbers k > 4 in a Collatz trajectory reaching k after starting at k+1.

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F a(n) = A070991(n+2) - 1.

%e a(1) = 5 because the orbit started at 6 = a(1) + 1 reaches 5:

%e   6 -> 3 -> 10 -> 5;

%e a(2) = 8 because the orbit started at 9 = a(2) + 1 reaches 8:

%e   9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8;

%e a(3) = 10 because the orbit started at 11 = a(3) + 1 reaches 10:

%e   11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10.

%o (PARI) collatz(start, target) = {my(old=start, new=0); while (new!=target && new!=1, if(old%2==0, new=old/2, new=3*old+1); old=new); new>1};

%o for (k=5, 10000, if(collatz(k+1, k), print1(k, ", ")))

%Y Cf. A006370, A006577, A070991, A070993, A355239, A355240, A355568.

%K nonn,more

%O 1,1

%A _Hugo Pfoertner_, Jul 10 2022