OFFSET
0,5
COMMENTS
A less natural variant of A051034, which counts the minimal number of primes that add up to n. The Goldbach conjecture implies that a(n) is nonzero for all n > 1.
The original definition was: "a(n) = -1 iff n is a prime, a(n) = 1 iff n is equal to the sum of three primes, a(n) = 2 iff n is equal to the sum of two primes, else a(n) = 0." However, the "iff"s do not make sense since all conditions can hold simultaneously. a(9) = 0 was obviously erroneous. More of the original data requires correction if "odd" is omitted in the second and/or added in the third condition, or if the conditions are tested in a different order.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
EXAMPLE
a(9) = 1 because 9 is not a prime but it is the sum of three odd primes, 9 = 3 + 3 + 3.
PROG
(PARI) a(n)={isprime(n)&&return(-1); forprime(p=3, n\3, forprime(q=p, (n-p)\2, isprime(n-p-q)&&return(1))); (n>1)*2}
CROSSREFS
KEYWORD
sign,less
AUTHOR
Giovanni Teofilatto, May 25 2005
EXTENSIONS
Edited, definition and a(9) corrected (following discussion and observations from several other Editors) by M. F. Hasler, Jan 08 2018
STATUS
approved