This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384181 #18 Jun 02 2025 18:11:27 %S A384181 2,3,71,97,179,181,211,223,251,283,431,503,577,827,857,971,1019,1021, %T A384181 1109,1213,1249,1259,1279,1289,1373,1427,1429,1483,1571,1609,1619, %U A384181 1637,1699,1709,1759,1801,2053,2129,2141,2213,2269,2281,2293,2297,2339,2381,2477,2503 %N A384181 Primes p such that k! + p or |k! - p| is composite for all k >= 0. %C A384181 It is unknown whether there exists a prime p such that k! + p is composite for all k > = 0 (see A082470). %C A384181 Every prime p in this list satisfies that at least one of the numbers k! + p, |k! - p| is composite; i.e., they cannot both be prime, for k >= 0. %e A384181 71 is in this sequence, since k! + 71 is prime only when k = 2, 5, 9, 14, 22, 43, 53 and 55, but |k! - 71| is composite for such values of k. %o A384181 (Python) %o A384181 from sympy import isprime, primerange, factorial %o A384181 def ok(p): %o A384181 return not any(isprime((fk := factorial(k)) + p) and isprime(abs(fk - p)) for k in range(1, p)) %o A384181 print([p for p in primerange(2, 500) if ok(p)]) %Y A384181 Cf. A082470, A352912. %K A384181 nonn %O A384181 1,1 %A A384181 _Gonzalo MartÃnez_, May 21 2025 %E A384181 a(17)-a(23) from _Sean A. Irvine_, May 28 2025 %E A384181 a(24)-a(48) from _Michael S. Branicky_, May 29 2025