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 A192367 Numbers k such that k! + 2*k + 1 is prime. 0
 0, 2, 3, 5, 6, 18, 44, 113, 2615, 16914 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Some of the larger entries may only correspond to probable primes. LINKS Table of n, a(n) for n=1..10. EXAMPLE 6! + 2*6 + 1 = 733 is prime, so 6 is in the sequence. MAPLE select(p -> isprime(factorial(p) + 2*p + 1), [\$0 .. 1000]) # Reza K Ghazi, Jul 11 2021 MATHEMATICA Select[Range[0, 1000], PrimeQ[#! + 2*# + 1] &] (* Reza K Ghazi, Jul 11 2021 *) PROG (Python) factor=1; for i in range(2, 10000): factor=factor*i if is_probable_prime(factor+2*i+1): #A Miller-Rabin primality test, with k=10 print i (Magma) [ n: n in [0..1000] | IsPrime(Factorial(n)+2*n+1) ]; // Klaus Brockhaus, Jul 02 2011 (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 */ (SageMath) [p for p in range(1000) if is_prime(factorial(p)+2*p+1)] # Reza K Ghazi, Jul 11 2021 CROSSREFS Cf. A073308 (k!+k+1 is prime). Sequence in context: A293027 A276353 A109628 * A227230 A102977 A238335 Adjacent sequences: A192364 A192365 A192366 * A192368 A192369 A192370 KEYWORD hard,nonn AUTHOR Julio Cesar Hernandez-Castro, Jun 29 2011 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 STATUS approved

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Last modified May 19 14:10 EDT 2024. Contains 372697 sequences. (Running on oeis4.)