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

1,1

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

Table of n, a(n) for n=1..34.

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.

Sequence in context: A094747 A300783 A359115 * A129738 A271314 A292006

Adjacent sequences: A287936 A287937 A287938 * A287940 A287941 A287942

Keyword

nonn

Author

Dmitry Kamenetsky, Jun 03 2017

Status

approved