A347267 a(n) is the first term of the n-th 3x+1 sequence that shares infinitely many 1's with the 3x+1 sequence that starts at 1.

1, 8, 10, 12, 13, 17, 22, 23, 27, 28, 29, 30, 36, 37, 38, 49, 50, 51, 64, 65, 66, 67, 71, 80, 84, 85, 86, 87, 89, 94, 95, 96, 103, 104, 106, 111, 113, 114, 115, 118, 119, 124, 125, 126, 136, 137, 138, 140, 141, 150, 151, 153, 156, 157, 158, 159, 164, 165, 166, 176, 180

Offset: 1

Author

Omar E. Pol, Aug 25 2021

Keywords

• nonn

Comments

a(n) is the first term of the row a(n) of the square array A347270.

Integers m such that A008908(m) == 1 (mod 3). - Michel Marcus, Aug 31 2021

Examples

			From _Michel Marcus_ and _Omar E. Pol_, Aug 31 2021: (Start)
Excerpt from A347270 array showing that the 3x+1 sequences that start at 1, 8, 10, 12 and 13 share infinitely many 1's.
   1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
   8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
  10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
  12, 6, 3,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
  13,40,20,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ... (End)
		

Links

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

Crossrefs

Companion of A347268 and A347269.

Cf. A006370, A008908, A033478, A033479, A075884, A076536, A153727, A347270.

Programs

PARI

f(n) = if (n%2, 3*n+1, n/2); \\ A006370
nb(n) = my(k=1, m=n); while (m!=1, k++; m=f(m)); k; \\ A008908
isok(m) = (nb(m) % 3) == 1; \\ Michel Marcus, Aug 31 2021

Extensions

More terms from Michel Marcus, Aug 31 2021