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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.

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=1, 10^5, N=n!+2*n+1; if(ispseudoprime(N), print1(n, ", ")));

/* use isprime() for stricter checking */ /* Joerg Arndt, Jul 03 2011 */

CROSSREFS

Cf. A073308 (numbers n such that n!+n+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 October 21 18:43 EDT 2019. Contains 328308 sequences. (Running on oeis4.)