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A175211

The finite sequence with the largest possible number of terms such that a(1) = a(2) = 1, for n >= 3, a(n) = prime p such that p = Sum_{i=1...k} a(n-i) for any k.

There are like shorter finite sequences with different terms: (1,1,2,3,5,11,19,41,71,131,281), (1,1,2,3,5,11,19,41,71,131,283), (1,1,2,3,5,11,19,41,79,139), (1,1,2,3,5,11,19,41,83), (1,1,2,3,5,11,23), (1,1,2,3,7,13,23,43,79), (1,1,2,3,7,13,23,43,89,181,313), (1,1,2,3,7,13,23,43,89,181,359).