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A259645 Numbers m such that m^2 + 1, 3*m - 1 and m^2 + m + 41 are all prime. 4

%I

%S 1,2,4,6,10,14,16,20,24,36,66,90,94,116,120,134,150,156,160,206,240,

%T 280,340,350,384,396,430,436,470,536,634,690,700,714,780,826,864,930,

%U 946,960,1004,1124,1150,1176,1294,1316,1376,1410,1430,1494,1644,1674

%N Numbers m such that m^2 + 1, 3*m - 1 and m^2 + m + 41 are all prime.

%C This sequence is infinite if the generalized Dickson's conjecture holds.

%H Reinhard Zumkeller, <a href="/A259645/b259645.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Bunyakovsky_conjecture">Bunyakovsky conjecture</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dickson&#39;s_conjecture">Dickson's conjecture</a>

%e . | (i, j, k) such that | corresponding

%e . | a(n) = A005574(i) | prime triples

%e . | | = A087370(j) | let m = a(n):

%e . n | a(n) | = A056561(k) | (m^2+1, 3*m-1, m^2+m+41)

%e . ---+------+---------------------+--------------------------

%e . 1 | 1 | (1, 1, 2) | (2, 2, 43)

%e . 2 | 2 | (2, 2, 3) | (5, 5, 47)

%e . 3 | 4 | (3, 3, 5) | (17, 11, 61)

%e . 4 | 6 | (4, 4, 7) | (37, 17, 83)

%e . 5 | 10 | (5, 6, 11) | (101, 29, 151)

%e . 6 | 14 | (6, 7, 13) | (197, 41, 251)

%e . 7 | 16 | (7, 8, 15) | (257, 47, 313)

%e . 8 | 20 | (8, 10, 21) | (401, 59, 461)

%e . 9 | 24 | (9, 11, 25) | (597, 71, 641)

%e . 10 | 36 | (11, 15, 37) | (1297, 107, 1373)

%e . 11 | 66 | (15, 24, 61) | (4357, 197, 4463)

%e . 12 | 90 | (18, 31, 79) | (8101, 269, 8231) .

%o (Haskell)

%o import Data.List.Ordered (isect)

%o a259645 n = a259645_list !! (n-1)

%o a259645_list = a005574_list `isect` a087370_list `isect` a056561_list

%Y Intersection of A005574, A087370 and A056561.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jul 03 2015

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Last modified December 5 06:36 EST 2020. Contains 338944 sequences. (Running on oeis4.)