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

1,1

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

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Sequence in context: A171928 A308259 A034879 * A071106 A157548 A134901

Adjacent sequences: A113585 A113586 A113587 * A113589 A113590 A113591

Keyword

nonn,base

Author

Amarnath Murthy, Nov 07 2005

Extensions

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

Status

approved