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

0,15

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.

Links

Table of n, a(n) for n=0..113.

Example

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.

Sequence in context: A055098 A297035 A055178 * A215887 A159451 A336682

Adjacent sequences: A174844 A174845 A174846 * A174848 A174849 A174850

Keyword

nonn

Author

Zak Seidov, Dec 01 2010

Status

approved