This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113588 #26 May 28 2021 20:11:07
%S A113588 3,6,720,362880,10888869450418352160768000000
%N A113588 a(1) = 3, a(n+1) = d!, where d is the sum of decimal digits of a(n).
%C A113588 The next term, a(6) = 108!, has 175 digits. - If one omits to take the sum of the digits, i.e., a(n+1)=a(n)!, where a(1)=3 is the least starting value that does not lead to a constant sequence, then the first three terms are the same but a(4) has 1747 digits. - _M. F. Hasler_, Mar 15 2016
%F A113588 a(n+1) = A000142(A007953(a(n))). - _M. F. Hasler_, Mar 15 2016
%e A113588 a(2) = 6;
%e A113588 a(3) = 6! = 720;
%e A113588 a(4) = (7+2+0)! = 9! = 362880;
%e A113588 a(5) = 27!.
%p A113588 A007953 := proc(n) add(i,i= convert(n,base,10)) ; end: A113588 := proc(n) option remember ; if n = 1 then 3; else factorial(A007953(A113588(n-1)) ) ; fi; end: for n from 1 to 6 do printf("%d,",A113588(n)) ; od: # _R. J. Mathar_, Feb 06 2008
%t A113588 NestList[Factorial@ Total[IntegerDigits@ #] &, 3, 4] (* _Michael De Vlieger_, Mar 15 2016 *)
%o A113588 (PARI) A007953(n,a=3)={for(i=2,n,a=sumdigits(a)!);a} \\ _M. F. Hasler_, Mar 15 2016
%K A113588 nonn,base
%O A113588 1,1
%A A113588 _Amarnath Murthy_, Nov 07 2005
%E A113588 More terms from _R. J. Mathar_, Feb 06 2008