A035065 Numbers k such that k! has a prime number of digits.

4, 5, 6, 8, 10, 14, 15, 20, 23, 27, 29, 33, 35, 39, 43, 51, 58, 68, 70, 84, 86, 89, 90, 95, 104, 107, 110, 111, 116, 117, 119, 120, 133, 134, 136, 139, 147, 150, 158, 159, 170, 183, 193, 199, 206, 211, 224, 229, 235, 239, 244, 249, 254, 270, 279, 282, 291, 299

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Examples

			a(1)=4 because 4! = 24 has 2 (a prime) digits.
23! = 25852016738884976640000 has exactly 23 digits!
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142, A034886, A035066, A067367.

Programs

Magma

[n: n in [1..300] | IsPrime(Floor(Log(10, Factorial(n))+1))]; // Vincenzo Librandi, Mar 28 2018

Maple

filter:= n -> isprime(1+ilog10(n!)):
select(filter, [$1..1000]); # Robert Israel, Mar 27 2018

Mathematica

Select[ Range[300], PrimeQ[ Floor[ Log[10, #! ] + 1]] & ]

PARI

isok(n) = isprime(#digits(n!)); \\ Michel Marcus, Mar 28 2018

Extensions

Offset corrected by Robert Israel, Mar 27 2018