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 A090106 #19 Sep 27 2024 07:22:41
%S A090106 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A090106 27,219
%N A090106 Values of k such that {P(k), P(k+1), ..., P(k+12)} are all prime numbers, where P(k) = k^2 + k + 41.
%C A090106 a(n) is the first argument providing 13 "polynomially consecutive" primes with respect to the polynomial x^2 + x + 41.
%C A090106 a(29) > 5*10^9, if it exists. - _Amiram Eldar_, Sep 27 2024
%e A090106 k = 219: {P(219), ..., P(231)} = {48221, ..., 53633}, i.e., 13 consecutive integer values substituted to P(x) = x^2 + x + 41 polynomial, all provide primes. The "classical case" includes one single 41-chain of PC-primes, see A055561.
%t A090106 Position[Times @@@ Partition[Table[Boole@PrimeQ[k^2 + k + 41], {k, 1, 1000}], 13, 1], 1] // Flatten (* _Amiram Eldar_, Sep 27 2024 *)
%o A090106 (PARI) isp(x) = isprime(x^2 + x + 41);
%o A090106 lista(kmax) = {my(v = vector(13, k, isp(k))); for(k = 14, kmax, if(vecprod(v) == 1, print1(k - 13, ", ")); v = concat(vecextract(v, "^1"), isp(k)));} \\ _Amiram Eldar_, Sep 27 2024
%Y A090106 Cf. A055561, A090101, A090102, A090562, A090563.
%K A090106 nonn,more
%O A090106 1,2
%A A090106 _Labos Elemer_, Dec 22 2003
%E A090106 2 wrong terms removed by _Amiram Eldar_, Sep 27 2024