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

0,3

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?

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000142, A004719, A243657.

Sequence in context: A256270 A374265 A243657 * A356757 A004154 A076126

Adjacent sequences: A321472 A321473 A321474 * A321476 A321477 A321478

Keyword

nonn,base

Author

Rémy Sigrist, Nov 11 2018

Status

approved