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A259645 Numbers m such that m^2 + 1, 3*m - 1 and m^2 + m + 41 are all prime. 6
1, 2, 4, 6, 10, 14, 16, 20, 24, 36, 66, 90, 94, 116, 120, 134, 150, 156, 160, 206, 240, 280, 340, 350, 384, 396, 430, 436, 470, 536, 634, 690, 700, 714, 780, 826, 864, 930, 946, 960, 1004, 1124, 1150, 1176, 1294, 1316, 1376, 1410, 1430, 1494, 1644, 1674 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence is infinite if the generalized Dickson's conjecture holds.
LINKS
EXAMPLE
. | (i, j, k) such that | corresponding
. | a(n) = A005574(i) | prime triples
. | | = A087370(j) | let m = a(n):
. n | a(n) | = A056561(k) | (m^2+1, 3*m-1, m^2+m+41)
. ---+------+---------------------+--------------------------
. 1 | 1 | (1, 1, 2) | (2, 2, 43)
. 2 | 2 | (2, 2, 3) | (5, 5, 47)
. 3 | 4 | (3, 3, 5) | (17, 11, 61)
. 4 | 6 | (4, 4, 7) | (37, 17, 83)
. 5 | 10 | (5, 6, 11) | (101, 29, 151)
. 6 | 14 | (6, 7, 13) | (197, 41, 251)
. 7 | 16 | (7, 8, 15) | (257, 47, 313)
. 8 | 20 | (8, 10, 21) | (401, 59, 461)
. 9 | 24 | (9, 11, 25) | (597, 71, 641)
. 10 | 36 | (11, 15, 37) | (1297, 107, 1373)
. 11 | 66 | (15, 24, 61) | (4357, 197, 4463)
. 12 | 90 | (18, 31, 79) | (8101, 269, 8231) .
PROG
(Haskell)
import Data.List.Ordered (isect)
a259645 n = a259645_list !! (n-1)
a259645_list = a005574_list `isect` a087370_list `isect` a056561_list
CROSSREFS
Intersection of A005574, A087370 and A056561.
Sequence in context: A089238 A005574 A109807 * A191113 A345211 A125964
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 03 2015
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)