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A243657
Zeroless factorials: a(0)=1; thereafter a(n) = noz(n*a(n-1)), where noz(n) = A004719(n) omits the zeros from n.
11
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
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
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jun 11 2014
STATUS
approved