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 A309285 #25 Jul 18 2022 22:48:37 %S A309285 341,29341,48354810571,493813961816587,32398013051587 %N A309285 a(n) is the smallest odd composite k such that prime(n)^((k-1)/2) == 1 (mod k) and q^((k-1)/2) == -1 (mod k) for every prime q < prime(n). %C A309285 a(n) is an Euler pseudoprime to base 2, so it is also a Fermat pseudoprime to base 2. %C A309285 This sequence is analogous to the sequence A307965 of primes. %C A309285 Conjecture: the smallest prime quadratic residue modulo a(n) is prime(n). %C A309285 a(6) <= 35141256146761030267, a(7) <= 4951782572086917319747. - _Daniel Suteu_, Jul 22 2019 %F A309285 According to the data, for n > 1, q^((a(n)-1)/2) == (q / a(n)) (mod a(n)) for every prime q <= prime(n), where (x / y) is the Jacobi symbol. %o A309285 (PARI) isok(n,k) = (k%2==1) && !isprime(k) && Mod(prime(n), k)^((k-1)/2) == Mod(1, k) && !forprime(q=2, prime(n)-1, if(Mod(q, k)^((k-1)/2) != Mod(-1, k), return(0))); %o A309285 a(n) = for(k=9, oo, if(isok(n, k), return(k))); \\ _Daniel Suteu_, Jul 22 2019 %Y A309285 Cf. A001567, A006970, A307798, A307965, A309284. %K A309285 nonn,hard,more %O A309285 1,1 %A A309285 _Thomas Ordowski_, Jul 21 2019 %E A309285 a(4)-a(5) from _Amiram Eldar_, Jul 21 2019