A227067 Least n-prime p such that the number of even n-primes (<= p) equals the number of odd n-primes (<= p).

3, 51, 32151, 300863849741

Offset

1,1

Comments

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.

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.

Links

Table of n, a(n) for n=1..4.

Example

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.

Mathematica

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}]

Crossrefs

Cf. A226833, A226835, A227069.

Sequence in context: A091502 A307022 A330302 * A261187 A347509 A273923

Adjacent sequences: A227064 A227065 A227066 * A227068 A227069 A227070

Keyword

nonn,hard,more

Author

T. D. Noe, Jul 03 2013

Extensions

a(4) from Donovan Johnson, Aug 13 2013

Status

approved