A359219 Starting numbers that require more iterations of the map x->A359194(x) (binary complement of 3n) to reach 0 than any smaller number.

0, 1, 2, 3, 4, 9, 11, 12, 17, 23, 28, 33, 74, 86, 180, 227, 350, 821, 3822, 4187, 5561, 6380, 6398, 22174, 22246, 26494, 34859, 49827, 70772, 103721, 104282, 204953, 213884, 225095, 407354, 425720

Offset

1,3

Comments

425720 after 10^10 iterations has not yet reached 0 and in general it is unknown whether every starting number does reach 0.

A359207(425720) = 87037147316. - Martin Ehrenstein, Jan 02 2023

Links

Table of n, a(n) for n=1..36.

Joshua Searle, Collatz-inspired sequences

Example

3 is a term because it requires 11 iterations to reach 0, which is more than any starting number less than 3.
0: (0) -- 0 terms
1: (1, 0) -- 1 term
2: (2, 1, 0) -- 2 terms
3: (3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0) -- 11 terms.

Prog

(Python)
from itertools import count, islice
def f(n): return 1 if n == 0 else (m:=3*n)^((1 << m.bit_length())-1)
def iters(n):
    i, fi = 0, n
    while fi != 0: i, fi = i+1, f(fi)
    return i
def agen(): # generator of terms
    record = -1
    for m in count(0):
        v = iters(m)
        if v > record: yield m; record = v
print(list(islice(agen(), 18))) # Michael S. Branicky, Dec 21 2022

Crossrefs

Cf. A035327, A359194, A359207, A359208, A359209, A359215, A359218, A359220, A359221, A359222.

Sequence in context: A283874 A263092 A118223 * A212989 A211546 A093514

Adjacent sequences: A359216 A359217 A359218 * A359220 A359221 A359222

Keyword

nonn,base,more

Author

Joshua Searle, Dec 21 2022

Extensions

a(27)-a(36) from Tom Duff (SeqFan mailing list, Dec 19 2022)

Status

approved