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A359222
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)).
3
0, 1, 2, 11, 80, 7572, 664475, 3180929, 120796790, 556068798, 1246707529, 87037147316
OFFSET
1,3
COMMENTS
a(12) found by Tom Duff (26 Dec 2022).
It is unknown whether all starting numbers reach 0.
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