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 A143537 #18 Mar 20 2020 02:17:57 %S A143537 0,1,1,2,2,1,2,2,1,0,3,3,2,1,1,3,3,2,1,1,0,4,4,3,2,2,1,1,4,4,3,2,2,1, %T A143537 1,0,4,4,3,2,2,1,1,0,0,4,4,3,2,2,1,1,0,0,0,5,5,4,3,3,2,2,1,1,1,1,5,5, %U A143537 4,3,3,2,2,1,1,1,1,0,6,6,5,4,4,3,3,2,2,2,2,1,1 %N A143537 Triangle read by rows: T(n,k) = number of primes in the interval [k..n], n >= 1, 1 <= k <= n. %C A143537 Old name: triangle read by rows, A000012 * A143536, 1<=k<=n. %F A143537 T(n,k) = pi(n) - pi(k-1), where pi = A000720. - _Ilya Gutkovskiy_, Mar 19 2020 %e A143537 Triangle T(n,k) begins: %e A143537 n\k 1 2 3 4 5 6 7 8 ... %e A143537 1: 0; %e A143537 2: 1, 1; %e A143537 3: 2, 2, 1; %e A143537 4: 2, 2, 1, 0; %e A143537 5: 3, 3, 2, 1, 1; %e A143537 6: 3, 3, 2, 1, 1, 0; %e A143537 7: 4, 4, 3, 2, 2, 1, 1; %e A143537 8: 4, 4, 3, 2, 2, 1, 1, 0; %e A143537 ... %Y A143537 Row sums are A034387. %Y A143537 Column k=1 gives A000720. %Y A143537 Main diagonal gives A010051. %Y A143537 T(2n,n) gives A035250. %Y A143537 Cf. A143536. %K A143537 nonn,tabl %O A143537 1,4 %A A143537 _Gary W. Adamson_, Aug 23 2008 %E A143537 New name and corrected by _Ilya Gutkovskiy_, Mar 19 2020