A359222 Number of steps to reach 0 from A359221(n) (Starting numbers that reach a new record high value during iteration by the map x->A359194(x)).

0, 1, 2, 11, 80, 7572, 664475, 3180929, 120796790, 556068798, 1246707529, 87037147316

Offset

1,3

Comments

a(12) found by Tom Duff (26 Dec 2022).

It is unknown whether all starting numbers reach 0.

Links

Table of n, a(n) for n=1..12.

Joshua Searle, Collatz-inspired sequences

Example

a(4) is the step count from the starting number A359221(4) = 3: (3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0) -- 11 steps, hence a(4) = 11.

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 itersmax(n):
    i, fi, m = 0, n, n
    while fi != 0: i, fi, m = i+1, f(fi), max(m, fi)
    return i, m
def agen(): # generator of terms
    record = -1
    for m in count(0):
        v, mx = itersmax(m)
        if mx > record:
            yield v # use m to obtain starting numbers
            record = mx
print(list(islice(agen(), 8))) # Michael S. Branicky, Dec 29 2022

Crossrefs

Step counts of A359221.

Cf. A035327, A359194, A359207, A359208, A359209, A359215, A359218, A359219, A359220, A359255.

Sequence in context: A056846 A277500 A197718 * A309417 A215654 A330677

Adjacent sequences: A359219 A359220 A359221 * A359223 A359224 A359225

Keyword

nonn,base,more,hard

Author

Joshua Searle, Dec 29 2022

Status

approved