A109885 Let n be an even integer > 2. Let PrimeP be the number of prime partition pairs {p,q} corresponding to n such that n = p + q, p and q are prime and p <= q. Let CompP be the number of composite partition pairs {r,s} corresponding to n such that n = r + s, r is prime, s is composite and r <= s. For what n's is 2*PrimeP > CompP?

4, 10, 22, 24, 34, 36, 48, 54, 60, 66, 72, 78, 84, 90, 102, 114, 120, 126, 144, 150, 156, 168, 180, 186, 198, 204, 210, 240, 246, 252, 270, 294, 300, 324, 330, 360, 378, 390, 420, 450, 462, 480, 510, 540, 546, 570, 600, 630, 660, 690, 714, 720, 750, 780, 840

Offset: 1

Author

Gilmar Rodriguez Pierluissi (gilmarlily(AT)yahoo.com), Aug 31 2005

Keywords

• nonn

Comments

Except for a(1), a(2) a(3) & a(5), a(n)==0 (mod 6). - Robert G. Wilson v

Programs

Mathematica

fQ[n_] := Block[{t = n - Prime@Range@PrimePi[n/2]}, 2Length[Select[t, PrimeQ]] > Length[t]]; Select[ 2Range[2, 434], fQ[ # ] &] (* Robert G. Wilson v, Nov 03 2005 *)

Extensions

Edited by Robert G. Wilson v, Nov 03 2005