A243657 - OEIS

%I #20 Jul 02 2024 10:19:49

%S 1,1,2,6,24,12,72,54,432,3888,3888,42768,513216,667188,934632,141948,

%T 2271168,3869856,6965748,132349212,264698424,555866694,1222967268,

%U 28128247164,67577931936,16894482984,439256557584,1185992754768,332779713354,965611687266,289683561798,89819415738

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

%C Zeroless analog of factorial numbers.

%C 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

%H N. J. A. Sloane, <a href="/A243657/b243657.txt">Table of n, a(n) for n = 0..10000</a>

%p 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;

%p t1:=[1]; for n from 1 to 50 do t1:=[op(t1),noz(n*t1[n])]; od: t1;

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

%o (Python)

%o from itertools import count, islice

%o def noz(n): return int(str(n).replace("0", ""))

%o def agen(): # generator of terms

%o     yield (an:=1)

%o     yield from (an:=noz(n*an) for n in count(1))

%o print(list(islice(agen(), 32))) # _Michael S. Branicky_, Jul 02 2024

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

%K nonn,base

%O 0,3

%A _N. J. A. Sloane_, Jun 11 2014