A212212 - OEIS

A212212

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

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

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OFFSET

1,39

COMMENTS

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

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. MR0337828 (49 #2597).

EXAMPLE

Array begins:

-1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, ...

-1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, ...

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

-1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, ...

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

-1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

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

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

...

MATHEMATICA