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 A338543 #25 Mar 03 2021 22:04:27
%S A338543 1,2,8,233,431
%N A338543 Numbers k such that 1 + Product_{i<k} prime(i) is divisible by prime(k).
%C A338543 Numbers k such that A062347(k-1) == -1 (mod prime(k)).
%H A338543 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3890719/is-510511-the-smallest-euclid-number-e-n-that-divides-by-the-next-prime-p/3890753#3890753">Is 510511 the smallest euclid number e_n that divides by the next prime p</a>.
%F A338543 a(n) = A081618(n)+1 for n >= 2.
%e A338543 a(3)=8 is a term because 1 + 2*3*5*7*11*13*17 = 510511 is divisible by prime(8)=19.
%p A338543 select(t -> 1+mul(ithprime(i),i=1..t-1) mod ithprime(t)=0, [$1..1000]);
%o A338543 (PARI) isok(n) = ((1+vecprod(primes(n-1))) % prime(n)) == 0; \\ _Michel Marcus_, Nov 03 2020
%Y A338543 Cf. A002110, A006862, A081618, A062347, A341805.
%K A338543 nonn,more
%O A338543 1,2
%A A338543 _Robert Israel_, Nov 01 2020