A174847 Number m of ways of representing 2n+1 as a sum of three primes such that all 3m primes are distinct.

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 6, 7, 8, 7, 7, 7, 7, 8, 8, 7, 8, 8, 8, 9, 8, 8, 9, 8, 8, 8, 8, 9, 9, 8, 9, 9, 9, 8, 9, 9, 9, 9, 10

Offset: 0

Author

Zak Seidov, Dec 01 2010

Keywords

• nonn

Comments

a(n) <= A102605(n) (Number of ways of writing 2n+1 as p+q+r where p,q,r are distinct primes).

Minimal numbers with n representation as sum of triple of primes such that all 3n primes are distinct are:

15,29,49,71,91,119,137,167,189,227,

255,273,317,345,375,369,435,483,495,535,

567,597,641,651,699,731,755,791,821,867,921,975.

Examples

			First number with m=1 is 15=3+5+7; for m=2,3,4 we have:
m=2: 29=3+7+19=5+11+13;  m=3: 49=3+5+41=5+7+37=13+17+19; m=4: 71=3+7+61=5+13+53=7+11+53=13+17+41.
		

Crossrefs

Cf. A102605.