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 A259645 #9 Apr 19 2025 18:04:05
%S A259645 1,2,4,6,10,14,16,20,24,36,66,90,94,116,120,134,150,156,160,206,240,
%T A259645 280,340,350,384,396,430,436,470,536,634,690,700,714,780,826,864,930,
%U A259645 946,960,1004,1124,1150,1176,1294,1316,1376,1410,1430,1494,1644,1674
%N A259645 Numbers m such that m^2 + 1, 3*m - 1 and m^2 + m + 41 are all prime.
%C A259645 This sequence is infinite if the generalized Dickson's conjecture holds.
%H A259645 Reinhard Zumkeller, <a href="/A259645/b259645.txt">Table of n, a(n) for n = 1..10000</a>
%H A259645 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bunyakovsky_conjecture">Bunyakovsky conjecture</a>
%H A259645 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dickson's_conjecture">Dickson's conjecture</a>
%e A259645 . | (i, j, k) such that | corresponding
%e A259645 . | a(n) = A005574(i) | prime triples
%e A259645 . | | = A087370(j) | let m = a(n):
%e A259645 . n | a(n) | = A056561(k) | (m^2+1, 3*m-1, m^2+m+41)
%e A259645 . ---+------+---------------------+--------------------------
%e A259645 . 1 | 1 | (1, 1, 2) | (2, 2, 43)
%e A259645 . 2 | 2 | (2, 2, 3) | (5, 5, 47)
%e A259645 . 3 | 4 | (3, 3, 5) | (17, 11, 61)
%e A259645 . 4 | 6 | (4, 4, 7) | (37, 17, 83)
%e A259645 . 5 | 10 | (5, 6, 11) | (101, 29, 151)
%e A259645 . 6 | 14 | (6, 7, 13) | (197, 41, 251)
%e A259645 . 7 | 16 | (7, 8, 15) | (257, 47, 313)
%e A259645 . 8 | 20 | (8, 10, 21) | (401, 59, 461)
%e A259645 . 9 | 24 | (9, 11, 25) | (597, 71, 641)
%e A259645 . 10 | 36 | (11, 15, 37) | (1297, 107, 1373)
%e A259645 . 11 | 66 | (15, 24, 61) | (4357, 197, 4463)
%e A259645 . 12 | 90 | (18, 31, 79) | (8101, 269, 8231) .
%t A259645 Select[Range[100], AllTrue[{#^2 + 1, 3 # - 1, #^2 + # + 41}, PrimeQ] &] (* _Robert Price_, Apr 19 2025 *)
%o A259645 (Haskell)
%o A259645 import Data.List.Ordered (isect)
%o A259645 a259645 n = a259645_list !! (n-1)
%o A259645 a259645_list = a005574_list `isect` a087370_list `isect` a056561_list
%Y A259645 Intersection of A005574, A087370 and A056561.
%K A259645 nonn
%O A259645 1,2
%A A259645 _Reinhard Zumkeller_, Jul 03 2015