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A377524
Number of steps for n to reach the minimum of its final cycle under iterations of the map (A123684): x->(3x-1)/2 if x odd, x/2 otherwise; or -1 if this never happens.
2
0, 1, 3, 2, 0, 4, 2, 3, 7, 1, 5, 5, 6, 3, 7, 4, 0, 8, 5, 2, 5, 6, 2, 6, 10, 7, 4, 4, 8, 8, 4, 5, 12, 1, 9, 9, 9, 6, 10, 3, 6, 6, 7, 7, 14, 3, 11, 7, 11, 11, 8, 8, 12, 5, 8, 5, 20, 9, 9, 9, 5, 5, 13, 6, 25, 13, 13, 2, 14, 10, 14, 10, 10, 10, 7, 7, 11, 11, 11, 4
OFFSET
1,3
COMMENTS
The currently known cycle minimums are 1, 5, 17 and there are no known a(n) = -1 (trajectory never reaches a cycle).
This sequence is one way to extend A006666 (number of Collatz (3x+1)/2 steps) to the negative numbers.
EXAMPLE
For n = 5, a(5) = 0 because 5 is already the minimum of its "final cycle".
For n = 12, a(12) = 6 because 12 takes 6 iterations to reach the minimum of its "final cycle": 12 -> 6 -> 3 -> 8 -> 4 -> 2 -> 1.
PROG
(Julia)
function three_x_minus_one_delay(n::Int)
count = 0
while (n != 1 && n != 5 && n != 17)
if (isodd(n))
n += n << 1 - 1
end
n >>= 1
count += 1
end
return count
end
CROSSREFS
Cf. A123684 ((3x-1)/2 map), A135730 (all steps).
Cf. A006666 (for (3x+1)/2).
Sequence in context: A290794 A328178 A127571 * A194662 A143612 A353160
KEYWORD
nonn
AUTHOR
Kevin Ge, Oct 28 2024
STATUS
approved