A113588 a(1) = 3, a(n+1) = d!, where d is the sum of decimal digits of a(n).

3, 6, 720, 362880, 10888869450418352160768000000

Offset: 1

Author

Amarnath Murthy, Nov 07 2005

Keywords

• nonn
• base

Comments

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

Examples

			a(2) = 6;
a(3) = 6! = 720;
a(4) = (7+2+0)! = 9! = 362880;
a(5) = 27!.
		

Programs

Maple

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

Mathematica

NestList[Factorial@ Total[IntegerDigits@ #] &, 3, 4] (* Michael De Vlieger, Mar 15 2016 *)

PARI

A007953(n,a=3)={for(i=2,n,a=sumdigits(a)!);a} \\ M. F. Hasler, Mar 15 2016

Formula

a(n+1) = A000142(A007953(a(n))). - M. F. Hasler, Mar 15 2016

Extensions

More terms from R. J. Mathar, Feb 06 2008