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 A271980 #33 Feb 16 2025 08:33:33 %S A271980 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,25,26,29, %T A271980 30,31,32,33,34,35,38,39,40,41,42,44,45,46,48,49,51,52,53,54,55,57,58, %U A271980 59,60,63,64,66,68,69,70,71,72,79,84,86,88,89,90,91,92 %N A271980 Numbers k such that 3*k^2 + 39*k + 37 is prime. %C A271980 From _Peter Bala_, Apr 16 2018: (Start) %C A271980 Let P(n) = 3*n^2 + 39*n + 37. The absolute values of the polynomial P(2*n - 29) = 12*n^2 - 270*n + 1429 for n from 0 to 27 are distinct primes, except at n = 14 when the value is 1. %C A271980 The absolute values of the polynomial 3*P((n - 20)/3) = n^2 - n - 269 for n from 0 to 42 are either prime or 3 times a prime. %C A271980 The absolute values of the polynomial 3*P((4*n - 89)/3) = 16*n^2 - 556*n + 4561 for n from 0 to 27 are either prime or 3 times a prime. (End) %H A271980 Robert Price, <a href="/A271980/b271980.txt">Table of n, a(n) for n = 1..3510</a> %H A271980 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomials</a> %e A271980 4 is in this sequence since 3*4^2 + 39*4 + 37 = 48+156+37 = 241 is prime. %t A271980 Select[Range[0, 100], PrimeQ[3*#^2 + 39*# + 37] &] %o A271980 (PARI) isok(n) = isprime(3*n^2 + 39*n + 37); \\ _Michel Marcus_, Apr 17 2016 %o A271980 (PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(3*n^2+39*n+37), print1(n, ", "))); \\ _Altug Alkan_, Apr 18 2016 %o A271980 (Magma) [n: n in [0..100] |IsPrime(3*n^2+39*n+37)]; // _Vincenzo Librandi_, Apr 19 2018 %Y A271980 Cf. A256585, A050265 - A050268, A005846, A007641, A007635, A048988. %K A271980 nonn,easy,less %O A271980 1,3 %A A271980 _Robert Price_, Apr 17 2016