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.
%I A157423 #5 Jul 19 2016 18:23:13
%S A157423 1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,
%T A157423 0,1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,1,0,1,0,0,1,1,0,
%U A157423 1,1,1,0,1,0,1,0,0,1
%N A157423 Triangle read by rows, T(n,k) = 0 if (n-k+1) is prime, else 1.
%C A157423 Row sums = A062298: (1, 1, 1, 2, 2, 3, 3, 4, 5, 6,...). Eigensequence of the triangle = A052284: (1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...).
%F A157423 Triangle read by rows, T(n,k) = 0 if (n-k+1) is prime, else 1. By columns, A005171 in every column: where A005171(k) = 0 if k is prime.
%e A157423 First few rows of the triangle =
%e A157423 1;
%e A157423 0, 1;
%e A157423 0, 0, 1;
%e A157423 1, 0, 0, 1;
%e A157423 0, 1, 0, 0, 1;
%e A157423 1, 0, 1, 0, 0, 1;
%e A157423 0, 1, 0, 1, 0, 0, 1;
%e A157423 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 1, 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1;
%e A157423 ...
%e A157423 Example: T(6,4) = 0 since (6 - 4 + 1) = 3, prime.
%t A157423 Table[If[PrimeQ[n-k+1],0,1],{n,15},{k,n}]//Flatten (* _Harvey P. Dale_, Jul 19 2016 *)
%Y A157423 Cf. A005171, A062298, A052284, A157424
%K A157423 nonn,tabl
%O A157423 1,1
%A A157423 _Gary W. Adamson_ & _Mats Granvik_, Feb 28 2009