cp's OEIS Frontend

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

%I A359219 #22 Jan 05 2023 18:58:25
%S A359219 0,1,2,3,4,9,11,12,17,23,28,33,74,86,180,227,350,821,3822,4187,5561,
%T A359219 6380,6398,22174,22246,26494,34859,49827,70772,103721,104282,204953,
%U A359219 213884,225095,407354,425720
%N A359219 Starting numbers that require more iterations of the map x->A359194(x) (binary complement of 3n) to reach 0 than any smaller number.
%C A359219 425720 after 10^10 iterations has not yet reached 0 and in general it is unknown whether every starting number does reach 0.
%C A359219 A359207(425720) = 87037147316. - _Martin Ehrenstein_, Jan 02 2023
%H A359219 Joshua Searle, <a href="https://qedscience.wordpress.com/2021/02/19/collatz-inspired-sequences/">Collatz-inspired sequences</a>
%e A359219 3 is a term because it requires 11 iterations to reach 0, which is more than any starting number less than 3.
%e A359219 0: (0) -- 0 terms
%e A359219 1: (1, 0) -- 1 term
%e A359219 2: (2, 1, 0) -- 2 terms
%e A359219 3: (3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0) -- 11 terms.
%o A359219 (Python)
%o A359219 from itertools import count, islice
%o A359219 def f(n): return 1 if n == 0 else (m:=3*n)^((1 << m.bit_length())-1)
%o A359219 def iters(n):
%o A359219     i, fi = 0, n
%o A359219     while fi != 0: i, fi = i+1, f(fi)
%o A359219     return i
%o A359219 def agen(): # generator of terms
%o A359219     record = -1
%o A359219     for m in count(0):
%o A359219         v = iters(m)
%o A359219         if v > record: yield m; record = v
%o A359219 print(list(islice(agen(), 18))) # _Michael S. Branicky_, Dec 21 2022
%Y A359219 Cf. A035327, A359194, A359207, A359208, A359209, A359215, A359218, A359220, A359221, A359222.
%K A359219 nonn,base,more
%O A359219 1,3
%A A359219 _Joshua Searle_, Dec 21 2022
%E A359219 a(27)-a(36) from _Tom Duff_ (SeqFan mailing list, Dec 19 2022)