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%I #29 Mar 21 2018 12:23:34
%S 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,
%T -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,
%U -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
%N 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.
%C 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.
%C 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.
%H Antti Karttunen, <a href="/A107393/b107393.txt">Table of n, a(n) for n = 0..65537</a>
%e a(9) = 1 because 9 is not a prime but it is the sum of three odd primes, 9 = 3 + 3 + 3.
%o (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}
%Y Cf. A051034.
%K sign,less
%O 0,5
%A _Giovanni Teofilatto_, May 25 2005
%E 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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