A227067 - OEIS

%I #11 Aug 13 2013 17:50:50

%S 3,51,32151,300863849741

%N Least n-prime p such that the number of even n-primes (<= p) equals the number of odd n-primes (<= p).

%C An n-prime is a number having n prime factors (counted multiply). For any n, the ratio of even n-primes to odd n-primes tends to decrease with the magnitude of the numbers. This may explain why the initial terms in A226835 are all even. The a(4) term is greater than 10^9.

%C There is only one other semiprime such that half of the previous semiprimes are odd: 62. For 3-primes, there are three other numbers: 32158, 32163, and 32170.

%e The first such prime is 3 because up to 3 there are an equal number of even and odd primes. The first such semiprime is 51 because there are 9 evens and 9 odds: 4, 6, 10, 14, 22, 26, 34, 38, 46 and 9, 15, 21, 25, 33, 35, 39, 49, 51.

%t nn = 3; Table[p = 1; odds = 0; evens = 0; While[odds*evens == 0 || odds != evens, p++; If[PrimeOmega[p] == n, If[OddQ[p], odds++, evens++]]]; p, {n, nn}]

%Y Cf. A226833, A226835, A227069.

%K nonn,hard,more

%O 1,1

%A _T. D. Noe_, Jul 03 2013

%E a(4) from _Donovan Johnson_, Aug 13 2013