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

Author

Dmitry Kamenetsky, May 05 2017

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A286263.