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%I #60 Jul 23 2023 01:54:23
%S 1,2,3,6,7,11,12,13,14,16,17,19,20,21,22,23,24,25,28,29,30,31,32,33,
%T 34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,53,55,56,57,58,59,64,
%U 65,66,67,72,73,74,75,77,78,81,84,85,86,87,90,91,92,93,94,95,98,100
%N Numbers k such that k^2 + k + 72491 is prime.
%C Of the first 10000 natural numbers, 4534 are in this sequence, making the density about 45%, quite large! (However, 72491 is not prime; it equals 71*1021, so no multiples of 71 or 1021 are in this sequence.)
%H Eric Chen, <a href="/A253239/b253239.txt">Table of n, a(n) for n = 1..4534</a> (all terms up to 10000)
%H C. Rivera, <a href="http://www.primepuzzles.net/problems/prob_012.htm">Prime producing polynomials</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-generating polynomial</a>
%e k k^2 + k + 72491
%e 0 72491 = 71*1021
%e 1 72493 (prime)
%e 2 72497 (prime)
%e 3 72503 (prime)
%e 4 72511 = 59*1229
%e 5 72521 = 47*1543
%e 6 72533 (prime)
%e 7 72547 (prime)
%e 8 72563 = 149*487
%e 9 72581 = 181*401
%e etc.
%p select(t -> isprime(t^2+t+72491), [$0..100]);
%t Select[Range[100], PrimeQ[#^2 + # + 72491] &]
%o (PARI) v=[ ]; for(n=0, 100, if(isprime(n^2+n+72491), v=concat(v, n), )); v
%o (Magma) [n: n in [0..100] | IsPrime(n^2 + n + 72491)]; // _Vincenzo Librandi_, Apr 20 2015
%Y Cf. A048097, A028823, A056561, A141489, A160548, A116206, A050267, A128878.
%K nonn,easy
%O 1,2
%A _Eric Chen_, Apr 19 2015
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