A355568 Numbers k > 4 in a Collatz trajectory reaching k after starting at k-1.

8, 10, 16, 20, 26, 34, 40, 52, 92, 122, 160, 167, 184, 244, 251, 334, 377, 412, 433, 488, 502, 650, 668, 866, 890, 976, 1154, 1186, 1300, 1336, 1732, 1780, 2308, 3644, 4858, 7288

Offset: 1

Author

Hugo Pfoertner, Jul 10 2022

Keywords

• nonn
• more

Examples

			8 is a term because the orbit started at 8 - 1 = 7 reaches 8:
  7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8;
10 is a term because it is in the orbit starting at 10 - 1 = 9:
  9 -> 28 -> 14 -> 7 -> 22 -> 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, A355569.

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) = A070993(n+1) + 1.