A359222 - OEIS

%I #12 Jan 05 2023 18:56:43

%S 0,1,2,11,80,7572,664475,3180929,120796790,556068798,1246707529,

%T 87037147316

%N Number of steps to reach 0 from A359221(n) (Starting numbers that reach a new record high value during iteration by the map x->A359194(x)).

%C a(12) found by Tom Duff (26 Dec 2022).

%C It is unknown whether all starting numbers reach 0.

%H Joshua Searle, <a href="https://qedscience.wordpress.com/2021/02/19/collatz-inspired-sequences/">Collatz-inspired sequences</a>

%e 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.

%o (Python)

%o from itertools import count, islice

%o def f(n): return 1 if n == 0 else (m:=3*n)^((1 << m.bit_length())-1)

%o def itersmax(n):

%o     i, fi, m = 0, n, n

%o     while fi != 0: i, fi, m = i+1, f(fi), max(m, fi)

%o     return i, m

%o def agen(): # generator of terms

%o     record = -1

%o     for m in count(0):

%o         v, mx = itersmax(m)

%o         if mx > record:

%o             yield v # use m to obtain starting numbers

%o             record = mx

%o print(list(islice(agen(), 8))) # _Michael S. Branicky_, Dec 29 2022

%Y Step counts of A359221.

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

%K nonn,base,more,hard

%O 1,3

%A _Joshua Searle_, Dec 29 2022