A192367 Numbers k such that k! + 2*k + 1 is prime.
0, 2, 3, 5, 6, 18, 44, 113, 2615, 16914
Offset: 1
Examples
6! + 2*6 + 1 = 733 is prime, so 6 is in the sequence.
Crossrefs
Cf. A073308 (k!+k+1 is prime).
Programs
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Magma
[ n: n in [0..1000] | IsPrime(Factorial(n)+2*n+1) ]; // Klaus Brockhaus, Jul 02 2011
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Maple
select(p -> isprime(factorial(p) + 2*p + 1), [$0 .. 1000]) # Reza K Ghazi, Jul 11 2021
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Mathematica
Select[Range[0, 1000], PrimeQ[#! + 2*# + 1] &] (* Reza K Ghazi, Jul 11 2021 *)
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PARI
for(n=0,10^5,N=n!+2*n+1;if(ispseudoprime(N),print1(n,", "))); /* use isprime() for stricter checking */ /* Joerg Arndt, Jul 03 2011 */
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Python
from sympy import isprime factor = 1; for i in range(0, 10000): if i < 2: factor = 1 else: factor = factor*i if isprime(factor + 2*i + 1): print(i, end=', ') -
SageMath
[p for p in range(1000) if is_prime(factorial(p)+2*p+1)] # Reza K Ghazi, Jul 11 2021
Extensions
0 added by Arkadiusz Wesolowski, Jun 29 2011
a(9) from Arkadiusz Wesolowski, Jul 02 2011
a(10) from Charles R Greathouse IV, Oct 14 2011
Comments