A202336 Number of digits in n^(n!).

1, 1, 1, 3, 15, 84, 561, 4260, 36413, 346276, 3628801, 41569064, 516929544, 6936548425, 99917483647, 1537944393896, 25193549397053, 437655212248536, 8036723680196724, 155554110186062367, 3165278489148945082, 67553429525569109411, 1508884070229326953381

Offset: 0

Author

Jacques ALARDET, Dec 17 2011

Keywords

• nonn
• base

Examples

			a(3) = 3 because 3^3! = 729 with 3 digits;
a(4) = 15 because 4^4! = 281474976710656 with 15 digits.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A053986, A202358.

Programs

Maple

a:= proc(n) local h;
      Digits:= 1000;
      1+ `if`(n=0, 0, floor(n!*simplify(log[10](n))))
    end:
seq(a(n), n=0..30); # Alois P. Heinz, Dec 17 2011

Mathematica

Table[IntegerLength[n^n!],{n,0,10}] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 19 2024 *)

Formula

a(n) = A055642(A053986(n)). - Michel Marcus, Aug 22 2013

Extensions

More terms from Alois P. Heinz, Dec 17 2011