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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Wikipedia, Bunyakovsky conjecture

Wikipedia, Dickson's conjecture

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 A125964 A288526

Adjacent sequences:  A259642 A259643 A259644 * A259646 A259647 A259648

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 03 2015

STATUS

approved

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Last modified January 20 17:41 EST 2018. Contains 297961 sequences.