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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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: A181952 A256270 A243657 * A004154 A076126 A263692

Adjacent sequences:  A321472 A321473 A321474 * A321476 A321477 A321478

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Nov 11 2018

STATUS

approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)