login
Integers k such that Sum_{i=1..k-1} (-1)^(i+1)*primepi((k-i+1)^2) = Sum_{i=1..k-1} (-1)^(i+1)*primepi((k-i)^2).
0

%I #28 Oct 06 2024 13:09:53

%S 1,3,8,16,36,38,70,108,116,148,251,280,1964

%N Integers k such that Sum_{i=1..k-1} (-1)^(i+1)*primepi((k-i+1)^2) = Sum_{i=1..k-1} (-1)^(i+1)*primepi((k-i)^2).

%F A_n = Sum_{i=1..n-1} (-1)^i * pi((n-i+1)^2);

%F B_n = Sum_{i=1..n-1} (-1)^i * pi((n-i)^2);

%F Sequence is S_n = {index(A_n - B_n) such that A_n - B_n = 0}.

%e For k = 3, pi(3^2)-pi(2^2) = 2 = pi(2^2)-pi(1^2), so 3 is a term.

%o (PARI) isok(k) = sum(i=1, k-1, (-1)^(i+1)*primepi((k-i+1)^2)) == sum(i=1, k-1, (-1)^(i+1)*primepi((k-i)^2)); \\ _Michel Marcus_, Aug 16 2022

%Y Cf. A000720.

%K nonn,more

%O 1,2

%A _Daniel Tisdale_, Nov 28 2011

%E New name and a(13) from _Michel Marcus_, Aug 16 2022