A107393 a(n) = -1 if n is a prime, else a(n) = 1 if n is the sum of three odd primes, else a(n) = 2 if n is the sum of two primes, else a(n) = 0.

0, 0, -1, -1, 2, -1, 2, -1, 2, 1, 2, -1, 2, -1, 2, 1, 2, -1, 2, -1, 2, 1, 2, -1, 2, 1, 2, 1, 2, -1, 2, -1, 2, 1, 2, 1, 2, -1, 2, 1, 2, -1, 2, -1, 2, 1, 2, -1, 2, 1, 2, 1, 2, -1, 2, 1, 2, 1, 2, -1, 2, -1, 2, 1, 2, 1, 2, -1, 2, 1, 2, -1, 2, -1, 2, 1, 2, 1, 2, -1, 2, 1, 2, -1, 2, 1, 2, 1, 2, -1, 2, 1, 2, 1, 2, 1, 2, -1, 2, 1, 2

Offset: 0

Author

Giovanni Teofilatto, May 25 2005

Keywords

• sign
• less

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.

Examples

			a(9) = 1 because 9 is not a prime but it is the sum of three odd primes, 9 = 3 + 3 + 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A051034.

Programs

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}

Extensions

Edited, definition and a(9) corrected (following discussion and observations from several other Editors) by M. F. Hasler, Jan 08 2018