A212213 Array read by antidiagonals: pi(n) + pi(k) - pi(n+k), where pi() = A000720.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0

Offset: 2

Author

N. J. A. Sloane, May 04 2012

Keywords

• nonn
• tabl
• nice

Comments

It is conjectured that pi(x) + pi(y) >= pi(x+y) for 1 < y <= x.

Examples

			Array begins:
  0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, ...
  0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, ...
  0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, ...
  0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, ...
  0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, ...
  1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, ...
  ...
		

References

• D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.5, p. 235.

Links

• G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
• P. Erdős and J. L. Selfridge, Complete prime subsets of consecutive integers. Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971), pp. 1-14. Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971.

Crossrefs

Cf. A000720, A047885, A047886, A060208, A212210-A212213.

Programs

Mathematica

t[n_, k_] := PrimePi[n] + PrimePi[k] - PrimePi[n + k]; Table[t[n - k + 2, k], {n, 0, 15}, {k, 2, n}] // Flatten (* Jean-François Alcover, Dec 31 2012 *)