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

%I A260689 #8 Nov 17 2015 19:02:14
%S A260689 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,
%T A260689 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,
%U A260689 15,21,33,35,3,21,27,33,1,5,11,19,25,29,31,37,3,15,27
%N A260689 Table read by rows: numbers m such that (2*n-m, 2*n+m) is a prime pair.
%C A260689 1 <= T(n,k) <= 2*n-3; T(n,2) > 3 for n > 3; all terms are odd;
%C A260689 A264526(n) = T(n,1);
%C A260689 A264527(n) = T(n,A069360(n));
%C A260689 T(A040040(n),1) = 1;
%C A260689 T(A088763(n),1) = 3.
%H A260689 Reinhard Zumkeller, <a href="/A260689/b260689.txt">Rows n = 2..1000 of triangle, flattened</a>
%H A260689 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A260689 .   n | T(n,k)          | (2*n-T(n,k), 2*n+T(n,k))       k=1..A069360(n)
%e A260689 . ----+-----------------+-----------------------------------------------
%e A260689 .   2 | 1               | (3,5)
%e A260689 .   3 | 1               | (5,7)
%e A260689 .   4 | 3,5             | (5,11) (3,13)
%e A260689 .   5 | 3,7             | (7,13) (3,17)
%e A260689 .   6 | 1,5,7           | (11,13) (7,17) (5,19)
%e A260689 .   7 | 3,9             | (11,17) (5,23)
%e A260689 .   8 | 3,13            | (13,19) (3,29)
%e A260689 .   9 | 1,5,11,13       | (17,19) (13,23) (7,29) (5,31)
%e A260689 .  10 | 3,9,17          | (17,23) (11,29) (3,37)
%e A260689 .  11 | 9,15,19         | (13,31) (7,37) (3,41)
%e A260689 .  12 | 5,7,13,17,19    | (19,29) (17,31) (11,37) (7,41) (5,43)
%e A260689 .  13 | 3,15,21         | (23,29) (11,41) (5,47)
%e A260689 .  14 | 9,15,25         | (19,37) (13,43) (3,53)
%e A260689 .  15 | 1,7,11,13,17,23 | (29,31) (23,37) (19,41) (17,43) (13,47) (7,53)
%e A260689 .  16 | 9,15,21,27,29   | (23,41) (17,47) (11,53) (5,59) (3,61)
%e A260689 .  17 | 3,27            | (31,37) (7,61)
%e A260689 .  18 | 5,7,17,23,25,31 | (31,41) (29,43) (19,53) (13,59) (11,61) (5,67)
%e A260689 .  19 | 9,15,21,33,35   | (29,47) (23,53) (17,59) (5,71) (3,73)
%e A260689 .  20 | 3,21,27,33      | (37,43) (19,61) (13,67) (7,73) .
%o A260689 (Haskell)
%o A260689 a260689 n k = a260689_tabf !! (n-2) !! (k-1)
%o A260689 a260689_row n = [m | m <- [1, 3 .. 2 * n - 3],
%o A260689                      a010051' (2*n + m) == 1, a010051' (2*n - m) == 1]
%o A260689 a260689_tabf = map a260689_row [2..]
%Y A260689 Cf. A069360 (row lengths), A010051, A264526, A264527.
%K A260689 nonn,tabf
%O A260689 2,3
%A A260689 _Reinhard Zumkeller_, Nov 17 2015