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%I #2 Mar 30 2012 17:30:42
%S 2,2,5,2,5,2,17,83,3,3,5,2,29,2,3,11,3,3,11,23,7,5,7,11,5,3,7,3,13,3,
%T 13,5,7,17,5,3,5,73,13,5,7,5,7,5,7,29,7,53,11,29,17,31,3,23,3,47,97,5,
%U 29,2,3,37,13,2,3,17,19,5,19,71,3,47,5,19,3,59,23,89,7,19,11,37,53,3
%N The sum or half the sum of n consecutive primes starting at a(n) is prime.
%C This eliminates the impossibles out of A007610 and the 'or' in the title is the exclusive or.
%e a(3) = 5 because 5+7+11 = prime 23 and a(10) = 3 because 3+5+7+11+13+17+19+23+29+31 = 158 and half that or 79 is a prime.
%t Do[k = n; a = Table[Prime[i], {i, 1, n} ]; While[ !PrimeQ[Plus @@ a] && !PrimeQ[Plus @@ a/2], k++; a = Drop[a, 1]; a = Append[a, Prime[k]]]; Print[a[[1]]], {n, 1, 100} ]
%Y Cf. A007610.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Feb 16 2002
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