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 A090108 #13 Sep 27 2024 08:35:18
%S A090108 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 A090108 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A090108 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,106
%N A090108 Values of k such that {P(k), P(k+1), ..., P(k+8)} are all prime numbers, whereP(k) = k^2 - 79*k + 1601.
%C A090108 a(n) is the first argument providing 9 "polynomially consecutive" primes with respect to the polynomial x^2 - 79*x + 1601 described by Escott in 1899.
%H A090108 Amiram Eldar, <a href="/A090108/b090108.txt">Table of n, a(n) for n = 1..535</a>
%H A090108 E. B. Escott, <a href="https://archive.org/details/lintermdiairede03lemogoog/page/n336/mode/2up">Réponse 1133, Formule d'Euler x^2 + x + 41 et formules analogues</a>, L'Intermédiaire des mathématiciens, Vol. 6 (1899), pp. 10-11.
%e A090108 k = 263 provides a chain of 9 "polynomially consecutive" primes as follows: {49993, 50441, 50891, 51343, 51797, 52253, 52711, 53171, 53633}.
%t A090108 Position[Times @@@ Partition[Table[Boole@PrimeQ[k^2 - 79*k + 1601], {k, 1, 1000}], 9, 1], 1] // Flatten (* _Amiram Eldar_, Sep 27 2024 *)
%o A090108 (PARI) isp(x) = isprime(x^2 - 79*x + 1601);
%o A090108 lista(kmax) = {my(v = vector(9, k, isp(k))); for(k = 10, kmax, if(vecprod(v) == 1, print1(k - 9, ", ")); v = concat(vecextract(v, "^1"), isp(k)));} \\ _Amiram Eldar_, Sep 27 2024
%Y A090108 Cf. A055561, A090101, A090102, A090107, A090562, A090563.
%K A090108 nonn
%O A090108 1,2
%A A090108 _Labos Elemer_, Dec 29 2003