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 A047886 #18 Jul 02 2025 16:01:57
%S A047886 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 A047886 -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 A047886 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 A047886 Triangle read by rows: T(n,k) = pi(n+k) - pi(n) - pi(k), where pi() = A000720 (n >= 0, 0 <= k <= n).
%C A047886 T(n,0)=0; for n > 0: T(n,1)=A010051(n); T(n,n)=-A060208(n). - _Reinhard Zumkeller_, Apr 15 2008
%C A047886 A212210-A212213 are the preferred versions of this array.
%e A047886 Triangle begins
%e A047886 0;
%e A047886 0, 1;
%e A047886 0, 1, 0;
%e A047886 0, 0, 0, -1;
%e A047886 0, 1, 0, 0, 0;
%e A047886 0, 0, 0, -1, -1, -2;
%e A047886 ...
%t A047886 Flatten[Table[PrimePi[n+k]-PrimePi[n]-PrimePi[k],{n,0,20},{k,0,n}]] (* _Harvey P. Dale_, Feb 22 2012 *)
%Y A047886 Cf. A047885, A212210-A212213.
%K A047886 sign,easy,tabl
%O A047886 0,21
%A A047886 _N. J. A. Sloane_
%E A047886 More terms from _James Sellers_, Dec 22 1999