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A374265
Minimized zeroless factorials.
1
1, 1, 2, 6, 24, 12, 72, 54, 432, 3888, 3888, 42768, 47916, 62298, 872172, 13968, 221688, 57996, 143928, 134712, 269154, 563994, 1247868, 286344, 877356, 171864, 513324, 1252728, 3414474, 914616, 41868, 119178, 454716, 127188, 527832, 15642, 91332, 192924, 125892, 29718
OFFSET
0,3
COMMENTS
a(n) is the smallest f(n) such that f(0) = 1 and for i > 0, f(i) = OpNoz_i(i*f(i-1)),where OpNoz_i is a function that either removes zeros or keeps the value unchanged (the choice is made for each value of i).
Removing zeros at every i gives an upper bound a(n) <= A243657(n); is this a strict inequality for n >= 12?
Is this sequence bounded?
EXAMPLE
a(12) = 47916 via the path: 1, 1, 2, 6, 24, 12, 72, 504, 4032, 36288, 362880, 3991680, 47916.
PROG
(Python)
def a(n):
reach = {1}
for i in range(1, n+1):
newreach = set()
for m in reach:
newreach.update([m*i, int(str(m*i).replace('0', ''))])
reach = newreach
return min(reach)
KEYWORD
nonn,base
AUTHOR
Bryle Morga, Jul 02 2024
STATUS
approved