A212213 - OEIS

%I #22 Sep 06 2023 23:18:52

%S 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,

%T 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,

%U 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

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

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

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

%H G. C. Greubel, <a href="/A212213/b212213.txt">Table of n, a(n) for the first 100 rows, flattened</a>

%H P. Erdős and J. L. Selfridge, <a href="http://www.renyi.hu/~p_erdos/1971-03.pdf">Complete prime subsets of consecutive integers</a>. Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971), pp. 1-14. Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971.

%e Array begins:

%e   0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, ...

%e   0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, ...

%e   0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, ...

%e   0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, ...

%e   0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e   1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, ...

%e   1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, ...

%e   ...

%t 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 *)

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

%K nonn,tabl,nice

%O 2,23

%A _N. J. A. Sloane_, May 04 2012