A121611 - OEIS

%I #3 Mar 30 2012 17:26:21

%S 0,0,0,1,1,2,2,2,3,2,4,3,6,3,6,3,8,3,10,3,12,5,13,5,14,5,17,4,21,4,22,

%T 4,21,6,23,5,27,7,32,5,36,5,35,7,34,5,36,7,43,5,46,8,47,8,44,5,52,6,

%U 55,6,61,8,58,8,57,9,67,8,71,7,79,7,72,9,69,6,76,7,83,9,94,9,91,9,89,8,94,8

%N Number of ways to express n as an average of three distinct primes.

%C For odd n's a(n) are much larger than a(n-/+1). Cf. A061357 = number of ways n can be expressed as the mean of two distinct primes, A061357 = number of ways the even integer 2n can be written as the sum of two primes for all even integers >6.

%e a(4)=1 because 4 = (2+3+7)/3 (1 way),

%e a(6)=2 because 6 = (2+3+13)/3 = (2+5+11)/3 (2 ways)

%e a(9)=3 because 9 = (3+5+19)/3 = (3+7+17)/3 = (3+11+13)/3 (3 ways)

%e a(11)=4 because 11 = (3+7+23)/3 = (3+11+19)/3 = (3+13+17)/3 = (5+11+19)/3 (4 ways), etc.

%Y Cf. A061357, A061357.

%K nonn

%O 1,6

%A _Zak Seidov_, Sep 08 2006