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 A185657 Numbers n such that (n^2 + n + 41) / 43 is prime. 2
 41, 44, 84, 87, 127, 130, 170, 173, 213, 216, 256, 259, 299, 302, 342, 345, 385, 388, 428, 471, 474, 517, 557, 560, 600, 643, 646, 689, 729, 732, 772, 815, 818, 944, 947, 987, 990, 1030, 1033, 1073, 1076, 1119, 1159, 1202, 1205, 1248, 1288, 1291, 1331, 1377, 1463, 1503, 1546 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There exists an infinity of integers of the form (m^2 + m + 41) / 43 if we consider the numbers m of the form m = 1 + 43k => (m^2 + m + 41)/43 = k(43k+3)+1. It's highly probable that a(n) is infinite. From Robert Israel, Jul 09 2017: (Start) All terms == 1 or 41 (mod 43). Bunyakovsky's conjecture implies there are infinitely many terms in both these classes. (End) LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 MAPLE select(t -> isprime((t^2+t+41)/43), [seq(seq(43*j+k, k = [1, 41]), j=0..100)]); # Robert Israel, Jul 09 2017 MATHEMATICA lst={}; Do[If[PrimeQ[(n^2+n+41)/43], AppendTo[lst, n]], {n, 2000}]; lst Select[Range[1600], PrimeQ[(#^2+#+41)/43]&] (* Harvey P. Dale, Feb 12 2011 *) PROG (PARI) is(n)=isprime((n^2+n+41)/43) \\ Charles R Greathouse IV, Jun 13 2017 CROSSREFS Cf. A185658. Sequence in context: A161614 A106098 A155500 * A095515 A095507 A095499 Adjacent sequences: A185654 A185655 A185656 * A185658 A185659 A185660 KEYWORD nonn,easy AUTHOR Michel Lagneau, Feb 08 2011 STATUS approved

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Last modified April 24 00:30 EDT 2024. Contains 371917 sequences. (Running on oeis4.)