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A107393
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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.
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1
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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
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OFFSET
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0,5
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(9) = 1 because 9 is not a prime but it is the sum of three odd primes, 9 = 3 + 3 + 3.
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PROG
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(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}
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CROSSREFS
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KEYWORD
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sign,less
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AUTHOR
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EXTENSIONS
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Edited, definition and a(9) corrected (following discussion and observations from several other Editors) by M. F. Hasler, Jan 08 2018
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STATUS
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approved
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