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A035065
Numbers k such that k! has a prime number of digits.
5
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
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
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Nov 15 1998
EXTENSIONS
Offset corrected by Robert Israel, Mar 27 2018
STATUS
approved