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A321475 Zeroless factorials (version 2): a(0) = 1, and for any n > 0, a(n) = noz(1 * noz(2 * ... * noz((n-1) * n))), where noz(n) = A004719(n) omits the zeros from n.

%I A321475 #17 May 20 2024 04:40:17
%S A321475 1,1,2,6,24,12,72,54,432,3888,3888,399168,576,82728,879912,2397168,
%T A321475 337968,5924736,8851949568,143936352,31644,92589264,118459638,3698784,
%U A321475 1197539136,2387625984,954864,236271168,3573339984,238453776,69587928,142275168,33566976
%N A321475 Zeroless factorials (version 2): a(0) = 1, and for any n > 0, a(n) = noz(1 * noz(2 * ... * noz((n-1) * n))), where noz(n) = A004719(n) omits the zeros from n.
%C A321475 This sequence is a variant of A243657 where the multiplications are carried in the opposite order; as (i, j) -> noz(i * j) is not associative in general we obtain another sequence.
%C A321475 Is this sequence bounded?
%H A321475 Rémy Sigrist, <a href="/A321475/b321475.txt">Table of n, a(n) for n = 0..10000</a>
%F A321475 a(10^k) = a(10^k - 1) for any k >= 0.
%e A321475 For n = 12:
%e A321475 - noz(11 * 12) = noz(132) = 132,
%e A321475 - noz(10 * 132) = noz(1320) = 132,
%e A321475 - noz(9 * 132) = noz(1188) = 1188,
%e A321475 - noz(8 * 1188) = noz(9504) = 954,
%e A321475 - noz(7 * 954) = noz(6678) = 6678,
%e A321475 - noz(6 * 6678) = noz(40068) = 468,
%e A321475 - noz(5 * 468) = noz(2340) = 234,
%e A321475 - noz(4 * 234) = noz(936) = 936,
%e A321475 - noz(3 * 936) = noz(2808) = 288,
%e A321475 - noz(2 * 288) = noz(576) = 576,
%e A321475 - noz(1 * 576) = noz(576) = 576,
%e A321475 - hence a(12) = 576.
%t A321475 noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
%t A321475 A321475[n_] := If[n == 0, 1, Block[{k = n}, Nest[noz[--k * #] &, n, n-1]]];
%t A321475 Array[A321475, 50, 0] (* _Paolo Xausa_, May 20 2024 *)
%o A321475 (PARI) a(n, base=10) = my (f=max(1, n)); forstep (k=n-1, 2, -1, f = fromdigits(select(sign, digits(f*k, base)), base)); f
%Y A321475 Cf. A000142, A004719, A243657.
%K A321475 nonn,base
%O A321475 0,3
%A A321475 _Rémy Sigrist_, Nov 11 2018