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A116366 Triangle read by rows: even numbers as sums of two odd primes.

%I A116366 #18 Sep 08 2022 08:45:24
%S A116366 6,8,10,10,12,14,14,16,18,22,16,18,20,24,26,20,22,24,28,30,34,22,24,
%T A116366 26,30,32,36,38,26,28,30,34,36,40,42,46,32,34,36,40,42,46,48,52,58,34,
%U A116366 36,38,42,44,48,50,54,60,62,40,42,44,48,50,54,56,60,66,68,74,44,46,48,52,54,58,60,64,70,72,78,82
%N A116366 Triangle read by rows: even numbers as sums of two odd primes.
%C A116366 T(n,k) = 2*A065305(n,k) = A065342(n+1,k+1);
%C A116366 Row sums give A116367; central terms give A116368;
%C A116366 T(n,1) = A113935(n+1);
%C A116366 T(n,n-2) = A048448(n) for n>2;
%C A116366 T(n,n-1) = A001043(n) for n>1;
%C A116366 T(n,n) = A001747(n+2) = A100484(n+1).
%H A116366 G. C. Greubel, <a href="/A116366/b116366.txt">Rows n = 1..100 of triangle, flattened</a>
%H A116366 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F A116366 T(n,k) = prime(n+1) + prime(k+1), 1 <= k <= n.
%e A116366 Triangle begins:
%e A116366   6;
%e A116366   8,  10;
%e A116366   10, 12, 14;
%e A116366   14, 16, 18, 22;
%e A116366   16, 18, 20, 24, 26;
%e A116366   20, 22, 24, 28, 30, 34;
%e A116366   22, 24, 26, 30, 32, 36, 38;
%e A116366   26, 28, 30, 34, 36, 40, 42, 46;
%e A116366   32, 34, 36, 40, 42, 46, 48, 52, 58;
%e A116366   34, 36, 38, 42, 44, 48, 50, 54, 60, 62;
%e A116366   40, 42, 44, 48, 50, 54, 56, 60, 66, 68, 74;
%e A116366   44, 46, 48, 52, 54, 58, 60, 64, 70, 72, 78, 82; etc. - _Bruno Berselli_, Aug 16 2013
%t A116366 Table[Prime[n+1] + Prime[k+1], {n,1,12}, {k,1,n}]//Flatten (* _G. C. Greubel_, May 12 2019 *)
%o A116366 (Magma) [NthPrime(n+1)+NthPrime(k+1): k in [1..n], n in [1..15]]; // _Bruno Berselli_, Aug 16 2013
%o A116366 (PARI) {T(n,k) = prime(n+1) + prime(k+1)}; \\ _G. C. Greubel_, May 12 2019
%o A116366 (Sage) [[nth_prime(n+1) + nth_prime(k+1) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, May 12 2019
%Y A116366 Cf. A001043, A001747, A048448, A065305, A065342, A100484, A113935, A116367, A116368.
%K A116366 nonn,tabl
%O A116366 1,1
%A A116366 _Reinhard Zumkeller_, Feb 06 2006