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A359220 Number of steps to reach 0 from A359219(n) where A359219 are the starting numbers that require more iterations in the map x->A359194(x) than any smaller number.

%I A359220 #26 Jan 12 2023 02:27:50
%S A359220 0,1,2,11,12,13,19,80,81,83,7572,7573,7574,7578,7580,664475,664882,
%T A359220 3180929,3180930,3180931,3181981,3181988,3182002,3182226,120796790,
%U A359220 556068798,556068799,556068871,556068872,572086553,572086610,1246707529,1246707552,1246707555,1246707602
%N A359220 Number of steps to reach 0 from A359219(n) where A359219 are the starting numbers that require more iterations in the map x->A359194(x) than any smaller number.
%C A359220 It is unknown whether all starting numbers reach 0; the next term, a(36) depends on whether 425720 ever reaches 0 (see A359207). It remains nonzero after 10^10 iterations.
%C A359220 A359207(425720) = 87037147316. Calculated by Tom Duff (12/16/22) - _Joshua Searle_, Jan 10 2023
%C A359220 a(4) - a(7) only differ by a small fraction of their starting terms. The same is true for the terms in the intervals a(8) - a(10), a(11) - a(15), a(16) - a(17) and a(18) - a(24). It may also be true for a(26) - a(29), a(30) - a(31) and a(32) - a(35).
%H A359220 Joshua Searle, <a href="https://qedscience.wordpress.com/2021/02/19/collatz-inspired-sequences/">Collatz-inspired sequences</a>
%e A359220 a(4) is the step count from the starting number A359219(4) = 3: (3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0) -- 11 steps, hence a(4) = 11.
%o A359220 (Python)
%o A359220 from itertools import count, islice
%o A359220 def f(n): return 1 if n == 0 else (m:=3*n)^((1 << m.bit_length())-1)
%o A359220 def iters(n):
%o A359220     i, fi = 0, n
%o A359220     while fi != 0: i, fi = i+1, f(fi)
%o A359220     return i
%o A359220 def agen(): # generator of terms
%o A359220     record = -1
%o A359220     for m in count(0):
%o A359220         v = iters(m)
%o A359220         if v > record: yield v; record = v
%o A359220 print(list(islice(agen(), 18))) # _Michael S. Branicky_, Dec 21 2022
%Y A359220 Step counts of A359219.
%Y A359220 Cf. A035327, A359194, A359207, A359208, A359209, A359215, A359218, A359219, A359221.
%K A359220 nonn,base
%O A359220 1,3
%A A359220 _Joshua Searle_, Dec 21 2022
%E A359220 a(27) and beyond from Tom Duff (SeqFan mailing list, Dec 19 2022)