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%I #32 Sep 08 2022 08:46:16
%S 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 30,31,32,33,34,35,38,39,40,41,42,44,45,46,48,49,51,52,53,54,55,57,58,
%U 59,60,63,64,66,68,69,70,71,72,79,84,86,88,89,90,91,92
%N Numbers k such that 3*k^2 + 39*k + 37 is prime.
%C From _Peter Bala_, Apr 16 2018: (Start)
%C 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 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 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 Robert Price, <a href="/A271980/b271980.txt">Table of n, a(n) for n = 1..3510</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomials</a>
%e 4 is in this sequence since 3*4^2 + 39*4 + 37 = 48+156+37 = 241 is prime.
%t Select[Range[0, 100], PrimeQ[3*#^2 + 39*# + 37] &]
%o (PARI) isok(n) = isprime(3*n^2 + 39*n + 37); \\ _Michel Marcus_, Apr 17 2016
%o (PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(3*n^2+39*n+37), print1(n, ", "))); \\ _Altug Alkan_, Apr 18 2016
%o (Magma) [n: n in [0..100] |IsPrime(3*n^2+39*n+37)]; // _Vincenzo Librandi_, Apr 19 2018
%Y Cf. A256585, A050265 - A050268, A005846, A007641, A007635, A048988.
%K nonn,easy,less
%O 1,3
%A _Robert Price_, Apr 17 2016
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