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A359219
Starting numbers that require more iterations of the map x->A359194(x) (binary complement of 3n) to reach 0 than any smaller number.
4
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
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
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