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

1,3

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.

Links

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

Joshua Searle, Collatz-inspired sequences

Example

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.

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

Crossrefs

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

Sequence in context: A075269 A215602 A325628 * A228501 A089414 A260631

Adjacent sequences: A359218 A359219 A359220 * A359222 A359223 A359224

Keyword

nonn,base,more,hard

Author

Joshua Searle, Dec 22 2022

Status

approved