login
Numbers k such that 7*k! + 1 is prime.
9

%I #15 Jul 04 2024 19:58:55

%S 3,7,8,15,19,29,36,43,51,158,160,203,432,909,1235,3209,8715,9707

%N Numbers k such that 7*k! + 1 is prime.

%C a(17) > 5830. - _Jinyuan Wang_, Feb 05 2020

%C a(19) > 12000. - _Michael S. Branicky_, Jul 04 2024

%e k = 3 is here because 7*3! + 1 = 43 is prime.

%o (PARI) is(k) = ispseudoprime(7*k!+1); \\ _Jinyuan Wang_, Feb 05 2020

%o (Python)

%o from sympy import isprime

%o from math import factorial

%o def aupto(m): return [k for k in range(m+1) if isprime(7*factorial(k)+1)]

%o print(aupto(300)) # _Michael S. Branicky_, Mar 07 2021

%Y Cf. A002981, A051915, A076679, A076680, A076681, A076682, A178488, A180626, A126896.

%K nonn,more

%O 1,1

%A Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

%E a(17)-a(18) from _Michael S. Branicky_, Jul 04 2024