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Numbers k such that 4*k! - 1 is prime.
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%I #27 Jul 12 2024 01:14:02

%S 0,1,2,3,5,6,10,11,51,63,197,313,579,1264,2276,2669,4316,4382,4678,

%T 7907,10843

%N Numbers k such that 4*k! - 1 is prime.

%C a(19) > 4570. - _Jinyuan Wang_, Feb 04 2020

%e k = 5 is here because 4*5! - 1 = 479 is prime.

%p for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;

%t For[n = 0, True, n++, If[PrimeQ[4 n! - 1], Print[n]]] (* _Jean-François Alcover_, Sep 23 2015 *)

%o (PARI) is_A099350(n)=ispseudoprime(n!*4-1) \\ _M. F. Hasler_, Sep 20 2015

%Y Cf. A076680.

%Y Cf. A002982, A076133, A076134, A099351, A180627, A180628, A180629, A180630, A180631.

%K nonn,hard,more

%O 1,3

%A _Brian Kell_, Oct 12 2004

%E a(14) from _Alois P. Heinz_, Sep 21 2015

%E a(15)-a(16) from _Jean-François Alcover_, Sep 23 2015

%E a(17)-a(18) from _Jinyuan Wang_, Feb 04 2020

%E a(19) from _Michael S. Branicky_, May 16 2023

%E a(20)-a(21) from _Michael S. Branicky_, Jul 11 2024