OFFSET
1,3
COMMENTS
a(12) found by Tom Duff (26 Dec 2022).
It is unknown whether all starting numbers reach 0.
LINKS
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
KEYWORD
nonn,base,more,hard
AUTHOR
Joshua Searle, Dec 29 2022
STATUS
approved