This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The array begins as: 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 3, 2, 1, 2, 1, 2, 1, 1, 2, ... 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, ... 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 5, 3, 4, 2, 3, 1, 2, 1, ... 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 3, 2, 1, 2, 1, 1, 1, 2, 2, ... 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, ... ... A(2,2) = 3 since 3 primes are in arithmetic progression with a difference of 2 and the first term equal to the 2nd prime: 3, 5, and 7. A(6,3) = 5 since 5 primes are in arithmetic progression with a difference of 6 and the first term equal to the 3rd prime: 5, 11, 17, 23, and 29.
A[n_,k_]:=Module[{count=1,sum=Prime[k]},While[PrimeQ[sum+=n], count++]; count]; Table[A[n-k+1,k],{n,13},{k,n}]//Flatten