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