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A335361 Prime numbers p such that p!*i + 1 is composite for i = 1..p.

%I A335361 #41 Sep 14 2020 20:02:56
%S A335361 67,157,269,379,419,443,449,509,541,577,743,769,859,863,929,937,1009,
%T A335361 1087,1163,1213,1217,1367,1381,1481,1579,1733,1747,1753,1783,1787,
%U A335361 1877,1901,1997,2153
%N A335361 Prime numbers p such that p!*i + 1 is composite for i = 1..p.
%C A335361 Primes in A335233.
%t A335361 Select[Prime@ Range@ 100, (f = #!; NoneTrue[f*Range[#] + 1, PrimeQ ]) &] (* _Robert Price_, Sep 14 2020 *)
%o A335361 (Python)
%o A335361 from sympy import isprime, nextprime, factorial
%o A335361 A335361_list, p = [], 2
%o A335361 while p < 500:
%o A335361     f, g = factorial(p), 1
%o A335361     for i in range(1,p+1):
%o A335361         g += f
%o A335361         if isprime(g):
%o A335361             break
%o A335361     else:
%o A335361         A335361_list.append(p)
%o A335361     p = nextprime(p)
%o A335361 (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 A335361 Cf. A035093, A321805, A335233.
%K A335361 nonn,more
%O A335361 1,1
%A A335361 _Chai Wah Wu_, Jun 10 2020
%E A335361 a(34) from _Jinyuan Wang_, Jun 21 2020