A286269 The smallest weight possible for a cyclic prime vector of order n.

2, 8, 19, 48, 53, 108, 113, 210, 197, 510

Offset

1,1

Comments

A cyclic 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. Unlike normal prime vectors, here the sums are allowed to span from the end to the start of the array. The weight of the cyclic prime vector is the sum of its elements. For full details see Kamenetsky's paper.

Links

Table of n, a(n) for n=1..10.

Dmitry Kamenetsky, Prime sums of primes, arXiv:1703.06778 [math.HO], 2017.

Example

The best solution for n=5 is (5, 7, 17, 13, 11) with a weight of 53. This is a cyclic prime vector because all the generated sums are prime: 5+7+17=29, 7+17+13=37, 17+13+11=41, 13+11+5=29, 11+5+7=23, 5+7+17+13+11=53.

Crossrefs

Cf. A286263.

Sequence in context: A372485 A000158 A101427 * A126877 A107769 A026588

Adjacent sequences: A286266 A286267 A286268 * A286270 A286271 A286272

Keyword

nonn,more

Author

Dmitry Kamenetsky, May 05 2017

Status

approved