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A374265 Minimized zeroless factorials.

%I A374265 #29 Jul 24 2024 02:09:56
%S A374265 1,1,2,6,24,12,72,54,432,3888,3888,42768,47916,62298,872172,13968,
%T A374265 221688,57996,143928,134712,269154,563994,1247868,286344,877356,
%U A374265 171864,513324,1252728,3414474,914616,41868,119178,454716,127188,527832,15642,91332,192924,125892,29718
%N A374265 Minimized zeroless factorials.
%C A374265 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).
%C A374265 Removing zeros at every i gives an upper bound a(n) <= A243657(n); is this a strict inequality for n >= 12?
%C A374265 Is this sequence bounded?
%e A374265 a(12) = 47916 via the path: 1, 1, 2, 6, 24, 12, 72, 504, 4032, 36288, 362880, 3991680, 47916.
%o A374265 (Python)
%o A374265 def a(n):
%o A374265    reach = {1}
%o A374265    for i in range(1, n+1):
%o A374265       newreach = set()
%o A374265       for m in reach:
%o A374265          newreach.update([m*i, int(str(m*i).replace('0', ''))])
%o A374265       reach = newreach
%o A374265    return min(reach)
%Y A374265 Cf. A000142, A004719, A242350, A243063, A243657, A243658, A356757, A374266.
%K A374265 nonn,base
%O A374265 0,3
%A A374265 _Bryle Morga_, Jul 02 2024