A260689 Table read by rows: numbers m such that (2*n-m, 2*n+m) is a prime pair.

1, 1, 3, 5, 3, 7, 1, 5, 7, 3, 9, 3, 13, 1, 5, 11, 13, 3, 9, 17, 9, 15, 19, 5, 7, 13, 17, 19, 3, 15, 21, 9, 15, 25, 1, 7, 11, 13, 17, 23, 9, 15, 21, 27, 29, 3, 27, 5, 7, 17, 23, 25, 31, 9, 15, 21, 33, 35, 3, 21, 27, 33, 1, 5, 11, 19, 25, 29, 31, 37, 3, 15, 27

Offset

2,3

Comments

1 <= T(n,k) <= 2*n-3; T(n,2) > 3 for n > 3; all terms are odd;

A264526(n) = T(n,1);

A264527(n) = T(n,A069360(n));

T(A040040(n),1) = 1;

T(A088763(n),1) = 3.

Links

Reinhard Zumkeller, Rows n = 2..1000 of triangle, flattened

Index entries for sequences related to Goldbach conjecture

Example

.   n | T(n,k)          | (2*n-T(n,k), 2*n+T(n,k))       k=1..A069360(n)
. ----+-----------------+-----------------------------------------------
.   2 | 1               | (3,5)
.   3 | 1               | (5,7)
.   4 | 3,5             | (5,11) (3,13)
.   5 | 3,7             | (7,13) (3,17)
.   6 | 1,5,7           | (11,13) (7,17) (5,19)
.   7 | 3,9             | (11,17) (5,23)
.   8 | 3,13            | (13,19) (3,29)
.   9 | 1,5,11,13       | (17,19) (13,23) (7,29) (5,31)
.  10 | 3,9,17          | (17,23) (11,29) (3,37)
.  11 | 9,15,19         | (13,31) (7,37) (3,41)
.  12 | 5,7,13,17,19    | (19,29) (17,31) (11,37) (7,41) (5,43)
.  13 | 3,15,21         | (23,29) (11,41) (5,47)
.  14 | 9,15,25         | (19,37) (13,43) (3,53)
.  15 | 1,7,11,13,17,23 | (29,31) (23,37) (19,41) (17,43) (13,47) (7,53)
.  16 | 9,15,21,27,29   | (23,41) (17,47) (11,53) (5,59) (3,61)
.  17 | 3,27            | (31,37) (7,61)
.  18 | 5,7,17,23,25,31 | (31,41) (29,43) (19,53) (13,59) (11,61) (5,67)
.  19 | 9,15,21,33,35   | (29,47) (23,53) (17,59) (5,71) (3,73)
.  20 | 3,21,27,33      | (37,43) (19,61) (13,67) (7,73) .

Prog

(Haskell)
a260689 n k = a260689_tabf !! (n-2) !! (k-1)
a260689_row n = [m | m <- [1, 3 .. 2 * n - 3],
                     a010051' (2*n + m) == 1, a010051' (2*n - m) == 1]
a260689_tabf = map a260689_row [2..]

Crossrefs

Cf. A069360 (row lengths), A010051, A264526, A264527.

Sequence in context: A299418 A214456 A118271 * A328386 A378640 A095366

Adjacent sequences: A260686 A260687 A260688 * A260690 A260691 A260692

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Nov 17 2015

Status

approved