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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to factorial numbers

Example

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

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]] & ]

Prog

(PARI) isok(n) = isprime(#digits(n!)); \\ Michel Marcus, Mar 28 2018
(Magma) [n: n in [1..300] | IsPrime(Floor(Log(10, Factorial(n))+1))]; // Vincenzo Librandi, Mar 28 2018

Crossrefs

Cf. A000142, A034886, A035066, A067367.

Sequence in context: A274918 A277736 A287358 * A209722 A035067 A027698

Adjacent sequences: A035062 A035063 A035064 * A035066 A035067 A035068

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 1998

Extensions

Offset corrected by Robert Israel, Mar 27 2018

Status

approved