A286263 The smallest weight possible for a prime vector of order n.

2, 8, 19, 26, 43, 56, 79, 104, 127, 166, 223, 258, 307, 348

Offset: 1

Author

Dmitry Kamenetsky, May 05 2017

Keywords

• nonn
• more

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 Kamenetsky's paper.

Calculations by Kamenetsky and J. K. Andersen show that a(15-17) are likely to be 443, 522 and 641.

Calculations by J. K. Andersen show that a(18-21) are likely to be 762, 881, 1002 and 1259.

J. K. Andersen found the best upper bounds for a(22-23) as 1716 and 1931.

For odd n, a(n) <= A068873(n) (smallest prime which is a sum of n distinct primes).

For even n, a(n) <= A071148(n) (sum of the first n odd primes).

Examples

			The best solution for n=5 is (3,11,5,7,17) with a weight of 43. This is a prime vector because all the generated sums are prime: 3+11+5=19, 11+5+7=23, 5+7+17=29, 3+11+5+7+17=43.
		

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. A068873, A071148, A286269.