A374192 Number of iterations required to reach 1 or 10 in a modified Collatz trajectory where x -> x/2 if x is even, x -> x+1 if x is odd and not divisible by 3 and x -> 3x+1 if x is odd and divisible by 3; or a(n) = -1 if 1 or 10 is never reached.

0, 1, 1, 2, 3, 2, 4, 3, 7, 0, 4, 3, 6, 5, 7, 4, 9, 8, 2, 1, 7, 5, 5, 4, 8, 7, 11, 6, 9, 8, 6, 5, 11, 10, 10, 9, 4, 3, 12, 2, 9, 8, 7, 6, 13, 6, 6, 5, 10, 9, 16, 8, 13, 12, 8, 7, 10, 10, 10, 9, 8, 7, 9, 6, 13, 12, 12, 11, 11, 11, 11, 10, 6, 5, 14, 4, 14, 13, 4, 3

Offset: 1

Author

Gary Detlefs, Jun 30 2024

Keywords

• nonn

Comments

It is conjectured that this iteration always reaches one of two cycles [1,2] or [10,5,6,3].

Examples

			n=1 takes a(1) = 0 iterations to reach 1 or 10, since it's already 1.
n=9 takes a(9) = 7 iterations to reach 1, by 9,28,14,7,8,4,2,1.
n=15 takes a(15) = 7 iterations to reach 10, by 15,46,23,24,12,6,3,10.