A359221 Starting numbers which reach a new record high value when iterating the map x->A359194(x) (binary complement of 3n).

0, 1, 2, 3, 12, 28, 227, 821, 22246, 26494, 204953, 425720

Offset: 1

Author

Joshua Searle, Dec 22 2022

Keywords

• nonn
• base
• more
• hard

Comments

It is unknown whether all starting numbers reach 0.

103721 is not a term of this sequence despite having a trajectory of record length, because its maximum of 2.42...*10^14081 is lower than the previous record holder.

Examples

			Let S(x) = iteration sequence of A359194 starting with x; then
S(0) = (0), maximum = 0;
S(1) = (1, 0), maximum = 1;
S(2) = (2, 1, 0), maximum = 2;
S(3) = (3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0), maximum = 300;
Since S(3) contains a higher maximum than any lower positive starting integer, 3 is a term of this sequence.
		

Links

• Joshua Searle, Collatz-inspired sequences

Crossrefs

Cf. A035327, A359194, A359207, A359208, A359209, A359215, A359218, A359219, A359220, A359222, A359255.

Programs

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 m # use mx to obtain values
            record = mx
print(list(islice(agen(), 8))) # Michael S. Branicky, Dec 22 2022