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

Author

Reinhard Zumkeller, Nov 17 2015

Keywords

• nonn
• tabf

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.

Examples

			.   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) .
		

Links

• Reinhard Zumkeller, Rows n = 2..1000 of triangle, flattened
• Index entries for sequences related to Goldbach conjecture

Crossrefs

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

Programs

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..]