A243657 Zeroless factorials: a(0)=1; thereafter a(n) = noz(n*a(n-1)), where noz(n) = A004719(n) omits the zeros from n.

1, 1, 2, 6, 24, 12, 72, 54, 432, 3888, 3888, 42768, 513216, 667188, 934632, 141948, 2271168, 3869856, 6965748, 132349212, 264698424, 555866694, 1222967268, 28128247164, 67577931936, 16894482984, 439256557584, 1185992754768, 332779713354, 965611687266, 289683561798, 89819415738

Offset

0,3

Comments

Zeroless analog of factorial numbers.

A very crude calculation suggests a(n) may grow like n^10. I don't really believe that, but certainly a(n) grows very slowly in comparison with n!. - N. J. A. Sloane, Sep 03 2014

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Maple

noz:=proc(n) local a, t1, i, j; a:=0; t1:=convert(n, base, 10); for i from 1 to nops(t1) do j:=t1[nops(t1)+1-i]; if j <> 0 then a := 10*a+j; fi; od: a; end;
t1:=[1]; for n from 1 to 50 do t1:=[op(t1), noz(n*t1[n])]; od: t1;

Mathematica

nxt[{n_, a_}]:={n+1, FromDigits[DeleteCases[IntegerDigits[a(n+1)], 0]]}; NestList[nxt, {0, 1}, 40][[;; , 2]] (* Harvey P. Dale, Feb 13 2024 *)

Prog

(Python)
from itertools import count, islice
def noz(n): return int(str(n).replace("0", ""))
def agen(): # generator of terms
    yield (an:=1)
    yield from (an:=noz(n*an) for n in count(1))
print(list(islice(agen(), 32))) # Michael S. Branicky, Jul 02 2024

Crossrefs

Cf. A000142, A004719, A242350, A243063, A243658.

Sequence in context: A345902 A256270 A374265 * A321475 A356757 A004154

Adjacent sequences: A243654 A243655 A243656 * A243658 A243659 A243660

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 11 2014

Status

approved