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A287939 a(n) is the smallest unused odd prime such that (a(1), ..., a(n)) forms a prime vector. a(1)=3, a(2)=5.

%I A287939 #9 Jun 03 2017 11:14:31
%S A287939 3,5,11,7,41,19,23,61,29,151,137,79,1013,14347,43151,7873,82469,
%T A287939 444187,63680783,80158627,531845381,13726723,2948038229,341461831,
%U A287939 5391683657,4759989589,45033191681,3342118271593,57517957292507,25358009530039,2584135512217541,616856808553033,21225241347141287,10855325323825603
%N A287939 a(n) is the smallest unused odd prime such that (a(1), ..., a(n)) forms a prime vector. a(1)=3, a(2)=5.
%C A287939 A prime vector of order n is an array of n distinct primes P = (p_1, p_2, ..., p_n) such that every sum of an odd number of consecutive elements is also prime. The weight of the prime vector is the sum of its elements. For full details see the Kamenetsky paper.
%C A287939 As of June 2017, (a(1), ..., a(34)) is the longest known prime vector. It was found by J. K. Andersen in Rivera's Puzzle 875.
%C A287939 Can this sequence be extended infinitely?
%H A287939 Dmitry Kamenetsky, <a href="https://arxiv.org/abs/1703.06778">Prime sums of primes</a>, arXiv:1703.06778 [math.HO], 2017.
%H A287939 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_875.htm">Puzzle 875: Vector of primes that generates distinct primes</a>
%Y A287939 Cf. A286263, A287940.
%K A287939 nonn
%O A287939 1,1
%A A287939 _Dmitry Kamenetsky_, Jun 03 2017