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Numbers k such that pi(k) is even.
2

%I #10 Jun 23 2024 22:02:42

%S 1,3,4,7,8,9,10,13,14,15,16,19,20,21,22,29,30,37,38,39,40,43,44,45,46,

%T 53,54,55,56,57,58,61,62,63,64,65,66,71,72,79,80,81,82,89,90,91,92,93,

%U 94,95,96,101,102,107,108,113,114,115,116,117,118,119

%N Numbers k such that pi(k) is even.

%H Charles R Greathouse IV, <a href="/A057811/b057811.txt">Table of n, a(n) for n = 1..10000</a>

%H Ping Ngai Chung and Shiyu Li, <a href="http://www.emis.de/journals/INTEGERS/papers/n79/n79.Abstract.html"> On the residue classes of π(n) modulo t</a>, INTEGERS: Electronic Journal of Combinatorial Number Theory 13 (2013), A79.

%F Chang & Li show that a(n) < 64n + o(1), and a(n) < 8n + o(1) under the Hardy-Littlewood prime tuples conjecture. - _Charles R Greathouse IV_, Dec 19 2014

%t Select[Range[120],EvenQ[PrimePi[#]]&] (* _Harvey P. Dale_, Apr 10 2024 *)

%o (PARI) is(n)=primepi(n)%2==0 \\ _Charles R Greathouse IV_, Dec 19 2014

%Y Cf. A000720, A057812.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 07 2000