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

1,2

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

Links

Table of n, a(n) for n=1..61.

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

Example

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)

Prog

(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

Crossrefs

Companion of A347268 and A347269.

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

Sequence in context: A176815 A338473 A336143 * A220571 A033872 A080752

Adjacent sequences: A347264 A347265 A347266 * A347268 A347269 A347270

Keyword

nonn

Author

Omar E. Pol, Aug 25 2021

Extensions

More terms from Michel Marcus, Aug 31 2021

Status

approved