A047886 Triangle read by rows: T(n,k) = pi(n+k) - pi(n) - pi(k), where pi() = A000720 (n >= 0, 0 <= k <= n).

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, -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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy
• tabl

Comments

T(n,0)=0; for n > 0: T(n,1)=A010051(n); T(n,n)=-A060208(n). - Reinhard Zumkeller, Apr 15 2008

A212210-A212213 are the preferred versions of this array.

Examples

			Triangle begins
  0;
  0,  1;
  0,  1,  0;
  0,  0,  0, -1;
  0,  1,  0,  0,  0;
  0,  0,  0, -1, -1, -2;
  ...
		

Crossrefs

Cf. A047885, A212210-A212213.

Programs

Mathematica

Flatten[Table[PrimePi[n+k]-PrimePi[n]-PrimePi[k],{n,0,20},{k,0,n}]] (* Harvey P. Dale, Feb 22 2012 *)

Extensions

More terms from James Sellers, Dec 22 1999