|
|
A212212
|
|
Array read by antidiagonals: pi(n) + pi(k) - pi(n+k), where pi() = A000720.
|
|
3
|
|
|
-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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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
|
a[n_, k_] := PrimePi[n] + PrimePi[k] - PrimePi[n+k]; Flatten[ Table[a[n-k, k], {n, 1, 15}, {k, 1, n-1}]] (* Jean-François Alcover, Jul 18 2012 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|