%I #20 May 04 2024 14:55:46
%S 1,1,2,3,2,2,1,4,6,6,3,2,2,4,6,1,2,4,2,4,2,5,4,2,4,8,4,14,3,10,4,2,4,
%T 6,12,6,1,10,6,6,4,14,6,8,6,5,4,2,4,2,4,24,18,14,8,3,10,2,6,6,10,6,4,
%U 2,6,10,1,4,6,20,6,14,4,2,6,4,2,6,9,8,6,4,6
%N Triangle read by rows. T(n,k) = least m > 0 such that prime(n) + m * prime(k) and m * prime(n) + prime(k) are both prime numbers, 1 <= k < n.
%C Assuming Dickson's conjecture, T(n,k) always exists.
%C T(n,1) is odd.
%C T(n,k) is even for any k > 1.
%C A229980(n) = T(n+1, n) for any n > 0.
%H Rémy Sigrist, <a href="/A286657/b286657.txt">Rows n=1..100 of triangle, flattened</a>
%H OEIS Wiki, <a href="/wiki/Dickson%27s_conjecture">Dickson's conjecture</a>
%e prime(7) + m*prime(11) is prime for m = 2, 12, 24, 26, 30, ...
%e m*prime(7) + prime(11) is prime for m = 8, 14, 18, 24, 30, ...
%e Hence, T(11,7) = 24.
%e The triangle T(n,k) begins:
%e n\k 1 2 3 4 5 6 7 8 9
%e 1:
%e 2: 1
%e 3: 1 2
%e 4: 3 2 2
%e 5: 1 4 6 6
%e 6: 3 2 2 4 6
%e 7: 1 2 4 2 4 2
%e 8: 5 4 2 4 8 4 14
%e 9: 3 10 4 2 4 6 12 6
%e 10: 1 10 6 6 4 14 6 8 6
%o (PARI) t(n,k) = my (pn=prime(n), pk=prime(k), i=1); while (!isprime(pn+i*pk) || !isprime(i*pn+pk), i++); return (i)
%Y Cf. A229980.
%K nonn,tabl
%O 1,3
%A _Rémy Sigrist_, May 14 2017