%I #10 Sep 18 2021 04:20:35
%S 0,1,2,1,2,3,0,2,3,4,1,1,3,4,4,0,2,2,3,4,5,1,1,2,2,4,5,6,0,1,1,3,3,5,
%T 6,6,0,0,2,2,4,4,5,6,7,0,1,1,3,3,4,4,6,7,8,1,1,2,2,3,3,5,5,7,8,8,0,2,
%U 2,2,2,4,4,6,6,7,8,9,1,1,2,2,3,3,5,5,6,6,8,9,9,0,1,1,3,3,4,4,5,5,7,7,8,9,9
%N Triangle read by rows: T(n,k) is the number of primes not less than n-k and not greater than n+k, 0<=k<n.
%F T(n,0) = A010051(n); T(n,n-1) = A000720(2*n-1).
%e Triangle begins:
%e 0;
%e 1, 2;
%e 1, 2, 3;
%e 0, 2, 3, 4;
%e 1, 1, 3, 4, 4;
%e 0, 2, 2, 3, 4, 5;
%e ...
%t T[n_, k_] := PrimePi[n+k] - PrimePi[n-k-1];
%t Table[T[n, k], {n, 1, 14}, {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Sep 18 2021 *)
%Y Cf. A000720, A010051.
%K nonn,tabl
%O 1,3
%A _Reinhard Zumkeller_, Nov 03 2003
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