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Triangle read by rows: T(n,k) = pi(n+k) - pi(n) - pi(k), where pi() = A000720 (n >= 0, 0 <= k <= n).
7

%I #17 Mar 07 2020 01:10:44

%S 0,0,1,0,1,0,0,0,0,-1,0,1,0,0,0,0,0,0,-1,-1,-2,0,1,0,-1,-1,-1,-1,0,0,

%T -1,-2,-1,-2,-1,-2,0,0,-1,-1,-1,-1,-1,-2,-2,0,0,0,-1,0,-1,-1,-2,-1,-1,

%U 0,1,0,0,0,-1,-1,-1,-1,0,0,0,0,0,-1,-1,-2,-1,-2,-1,-1,-1,-2,0,1,0,-1

%N Triangle read by rows: T(n,k) = pi(n+k) - pi(n) - pi(k), where pi() = A000720 (n >= 0, 0 <= k <= n).

%C T(n,0)=0; for n > 0: T(n,1)=A010051(n); T(n,n)=-A060208(n). - _Reinhard Zumkeller_, Apr 15 2008

%C A212210-A212213 are the preferred versions of this array.

%e Triangle begins

%e 0;

%e 0, 1;

%e 0, 1, 0;

%e 0, 0, 0, -1;

%e 0, 1, 0, 0, 0;

%e 0, 0, 0, -1, -1, -2;

%e ...

%t Flatten[Table[PrimePi[n+k]-PrimePi[n]-PrimePi[k],{n,0,20},{k,0,n}]] (* _Harvey P. Dale_, Feb 22 2012 *)

%Y Cf. A047885, A212210-A212213.

%K sign,easy,tabl

%O 0,21

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Dec 22 1999