A121611 Number of ways to express n as an average of three distinct primes.

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, 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, 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

Offset

1,6

Comments

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.

Links

Table of n, a(n) for n=1..88.

Example

a(4)=1 because 4 = (2+3+7)/3 (1 way),
a(6)=2 because 6 = (2+3+13)/3 = (2+5+11)/3 (2 ways)
a(9)=3 because 9 = (3+5+19)/3 = (3+7+17)/3 = (3+11+13)/3 (3 ways)
a(11)=4 because 11 = (3+7+23)/3 = (3+11+19)/3 = (3+13+17)/3 = (5+11+19)/3 (4 ways), etc.

Crossrefs

Cf. A061357, A061357.

Sequence in context: A346598 A035433 A029199 * A360106 A300066 A286545

Adjacent sequences: A121608 A121609 A121610 * A121612 A121613 A121614

Keyword

nonn

Author

Zak Seidov, Sep 08 2006

Status

approved