login
A347269
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 4.
3
4, 5, 6, 11, 14, 15, 18, 19, 25, 32, 33, 40, 42, 43, 47, 48, 52, 53, 57, 59, 62, 63, 68, 69, 70, 75, 78, 79, 82, 83, 88, 90, 91, 92, 93, 105, 108, 109, 110, 112, 116, 117, 120, 121, 122, 135, 139, 144, 145, 146, 147, 148, 149, 152, 154, 161, 162, 163, 175, 185, 187, 191, 193
OFFSET
1,1
COMMENTS
a(n) is the first term of the row a(n) of the square array A347270.
Integers m such that A008908(m) == 0 (mod 3). - Michel Marcus, Aug 31 2021
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 4, 5, 6, 11 and 14 share infinitely many 1's.
4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
6, 3,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
11,34,17,52,26,13,40,20,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
14, 7,22,11,34,17,52,26,13,40,20,10, 5,16, 8, 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) == 0; \\ Michel Marcus, Aug 31 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Aug 25 2021
EXTENSIONS
More terms from Michel Marcus, Aug 31 2021
STATUS
approved