

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, 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
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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 A103159
Adjacent sequences: A174844 A174845 A174846 * A174848 A174849 A174850


KEYWORD

nonn


AUTHOR

Zak Seidov, Dec 01 2010


STATUS

approved



