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

1,4

Comments

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

Links

Table of n, a(n) for n=1..80.

Example

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.

Crossrefs

Sequence in context: A363159 A378161 A261172 * A134834 A035583 A145178

Adjacent sequences: A374189 A374190 A374191 * A374193 A374194 A374195

Keyword

nonn

Author

Gary Detlefs, Jun 30 2024

Status

approved