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%I #41 Sep 14 2020 20:02:56
%S 67,157,269,379,419,443,449,509,541,577,743,769,859,863,929,937,1009,
%T 1087,1163,1213,1217,1367,1381,1481,1579,1733,1747,1753,1783,1787,
%U 1877,1901,1997,2153
%N Prime numbers p such that p!*i + 1 is composite for i = 1..p.
%C Primes in A335233.
%t Select[Prime@ Range@ 100, (f = #!; NoneTrue[f*Range[#] + 1, PrimeQ ]) &] (* _Robert Price_, Sep 14 2020 *)
%o (Python)
%o from sympy import isprime, nextprime, factorial
%o A335361_list, p = [], 2
%o while p < 500:
%o f, g = factorial(p), 1
%o for i in range(1,p+1):
%o g += f
%o if isprime(g):
%o break
%o else:
%o A335361_list.append(p)
%o p = nextprime(p)
%o (PARI) is(p) = if(isprime(p), for(i=1, p, if(ispseudoprime(i*p!+1), return(0))); 1, 0); \\ _Jinyuan Wang_, Jun 21 2020
%Y Cf. A035093, A321805, A335233.
%K nonn,more
%O 1,1
%A _Chai Wah Wu_, Jun 10 2020
%E a(34) from _Jinyuan Wang_, Jun 21 2020
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