The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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