OFFSET
0,6
COMMENTS
Goldbach conjectured that every integer >5 is the sum of three primes. 6=2+2+2, 7=2+2+3, 8=2+3+3, 9=3+3+3=2+2+5,...
LINKS
Sean A. Irvine, Table of n, a(n) for n = 0..10000
EXAMPLE
From Sean A. Irvine, Oct 15 2022: (Start)
For an integer n we consider representations of n as the sum of three primes. We are looking for a prime that occurs in the representations as many consecutive integers starting from n+1 as possible.
a(5) = 7 because we can write 6=2+2+2, 7=2+2+3, 8=2+3+3, 9=2+2+5, 10=2+3+5, 11=2+2+7, 12=2+5+5 (all of which contain the prime 2), but there is no way to write 13=2+p+q for primes p and q.
Similarly, a(6) = 7 because we can write 7=2+2+3, 8=2+3+3, 9=3+3+3, 10=2+3+5, 11=3+3+5, 12=2+3+7, 13=3+5+5 (all of which contain the prime 3), but there is no way to write 14=3+p+q for primes p and q.
Notice the representations used for a(5) and a(6) differ for 9, 11, and 12. In general, it is necessary to consider all possible representations for each number and all the primes occurring in those representations as potential candidates.
(End)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Mar 05 2001
STATUS
approved