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.

1, 1, 2, 6, 24, 12, 72, 54, 432, 3888, 3888, 399168, 576, 82728, 879912, 2397168, 337968, 5924736, 8851949568, 143936352, 31644, 92589264, 118459638, 3698784, 1197539136, 2387625984, 954864, 236271168, 3573339984, 238453776, 69587928, 142275168, 33566976

Offset: 0

Author

Rémy Sigrist, Nov 11 2018

Keywords

• nonn
• base

Comments

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.

Is this sequence bounded?

Examples

			For n = 12:
- noz(11 * 12) = noz(132) = 132,
- noz(10 * 132) = noz(1320) = 132,
- noz(9 * 132) = noz(1188) = 1188,
- noz(8 * 1188) = noz(9504) = 954,
- noz(7 * 954) = noz(6678) = 6678,
- noz(6 * 6678) = noz(40068) = 468,
- noz(5 * 468) = noz(2340) = 234,
- noz(4 * 234) = noz(936) = 936,
- noz(3 * 936) = noz(2808) = 288,
- noz(2 * 288) = noz(576) = 576,
- noz(1 * 576) = noz(576) = 576,
- hence a(12) = 576.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000142, A004719, A243657.

Programs

Mathematica

noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
A321475[n_] := If[n == 0, 1, Block[{k = n}, Nest[noz[--k * #] &, n, n-1]]];
Array[A321475, 50, 0] (* Paolo Xausa, May 20 2024 *)

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

Formula

a(10^k) = a(10^k - 1) for any k >= 0.