A355569 Numbers k > 4 in a Collatz trajectory reaching k after starting at k+1.

5, 8, 10, 13, 16, 17, 38, 40, 46, 53, 56, 58, 61, 70, 80, 88, 106, 107, 160, 251, 283, 377, 638, 650, 958, 976, 1367, 1438, 1822, 2158, 2429, 2734, 3238, 4102, 4616, 4858, 6154, 7288, 9232

Offset: 1

Author

Hugo Pfoertner, Jul 10 2022

Keywords

• nonn
• more

Examples

			a(1) = 5 because the orbit started at 6 = a(1) + 1 reaches 5:
  6 -> 3 -> 10 -> 5;
a(2) = 8 because the orbit started at 9 = a(2) + 1 reaches 8:
  9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8;
a(3) = 10 because the orbit started at 11 = a(3) + 1 reaches 10:
  11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10.
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

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

Programs

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};
for (k=5, 10000, if(collatz(k+1, k), print1(k, ", ")))

Formula

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