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Primes whose factorials end with a prime number of trailing 0's.
2

%I #17 May 03 2024 04:18:15

%S 11,13,17,19,31,59,83,127,151,173,179,197,199,223,293,367,397,421,439,

%T 449,461,463,557,569,607,617,619,631,659,733,773,797,853,919,941,967,

%U 1013,1039,1061,1063,1087,1097,1123,1181,1259,1399,1423,1447,1543,1567

%N Primes whose factorials end with a prime number of trailing 0's.

%C For the corresponding prime number of trailing end 0's, see A181577.

%H Amiram Eldar, <a href="/A181576/b181576.txt">Table of n, a(n) for n = 1..10000</a>

%F A027868(a(n)) = A181577(n). - _Amiram Eldar_, May 03 2024

%e The factorial 2! = 2 ends with 0 zeros, so the prime 2 is not in the sequence because 0 is not a prime.

%e The factorial 5! = 120 ends with 1 zero, so the prime 5 is not in the sequence because 1 is not a prime.

%e The factorial 11! = 39916800 ends with 2 zeros, so the prime 11 is in the sequence because 2 is a prime.

%t Select[ Prime@ Range@ 250, PrimeQ@ IntegerExponent[ #! ] &] (* _Robert G. Wilson v_, Nov 06 2010 *)

%o (PARI) is(p) = isprime(p) && isprime((p - sumdigits(p, 5))/4); \\ _Amiram Eldar_, May 03 2024

%Y Cf. A027868, A039716, A181577.

%K nonn,base

%O 1,1

%A _Lekraj Beedassy_, Nov 02 2010

%E More terms from _Robert G. Wilson v_, Nov 06 2010