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.

3, 5, 11, 7, 41, 19, 23, 61, 29, 151, 137, 79, 1013, 14347, 43151, 7873, 82469, 444187, 63680783, 80158627, 531845381, 13726723, 2948038229, 341461831, 5391683657, 4759989589, 45033191681, 3342118271593, 57517957292507, 25358009530039, 2584135512217541, 616856808553033, 21225241347141287, 10855325323825603

Offset: 1

Author

Dmitry Kamenetsky, Jun 03 2017

Keywords

• nonn

Comments

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.

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.

Can this sequence be extended infinitely?

Links

• Dmitry Kamenetsky, Prime sums of primes, arXiv:1703.06778 [math.HO], 2017.
• Carlos Rivera, Puzzle 875: Vector of primes that generates distinct primes

Crossrefs

Cf. A286263, A287940.