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A131424 Triangle read by rows: T(n,k) = prime(n) + prime(k) - 3, 1 <= k <= n.

%I A131424 #15 Feb 20 2025 22:23:02
%S A131424 1,2,3,4,5,7,6,7,9,11,10,11,13,15,19,12,13,15,17,21,23,16,17,19,21,25,
%T A131424 27,31,18,19,21,23,27,29,33,35,22,23,25,27,31,33,37,39,43,28,29,31,33,
%U A131424 37,39,43,45,49,55,30,31,33,35,39,41,45,47,51,57,59
%N A131424 Triangle read by rows: T(n,k) = prime(n) + prime(k) - 3, 1 <= k <= n.
%C A131424 Left border = A006093, (primes - 1): (1, 2, 4, 6, 10, 12, ...). Right border = A131426 (2*primes - 3): (1, 3, 7, 11, 19, 23, 31, ...). Row sums = A131425: (1, 5, 16, 33, 68, 101, 156, ...).
%H A131424 Andrew Howroyd, <a href="/A131424/b131424.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%F A131424 Equals (A000012 * A127640) + (A127640 * A000012) - 3*A000012 as infinite lower triangular matrices.
%e A131424 First few rows of the triangle are:
%e A131424    1;
%e A131424    2,  3;
%e A131424    4,  5,  7;
%e A131424    6,  7,  9, 11;
%e A131424   10, 11, 13, 15, 19;
%e A131424   12, 13, 15, 17, 21, 23;
%e A131424   16, 17, 19, 21, 25, 27, 31;
%e A131424   18, 19, 21, 23, 27, 29, 33, 35;
%e A131424   22, 23, 25, 27, 31, 33, 37, 39, 43;
%e A131424 ...
%t A131424 T[n_,k_]:=Prime[n]+Prime[k]-3;Table[T[n,k],{n,11},{k,n}]//Flatten (* _James C. McMahon_, Feb 20 2025 *)
%o A131424 (PARI) T(n,k) = if(k<=n, prime(n) + prime(k) - 3, 0) \\ _Andrew Howroyd_, Sep 01 2018
%Y A131424 Row sums are A131425.
%Y A131424 Cf. A127640, A131426, A006093, A000040.
%K A131424 nonn,tabl
%O A131424 1,2
%A A131424 _Gary W. Adamson_, Jul 10 2007
%E A131424 Name clarified and terms a(56) and beyond from _Andrew Howroyd_, Sep 01 2018