A286263 -id:A286263 - cp's OEIS frontend

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

Dmitry Kamenetsky, May 05 2017

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.

			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.

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

Cf. A286263.

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.

Original entry on oeis.org

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

Dmitry Kamenetsky, Jun 03 2017

nonn

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?

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

Cf. A286263, A287940.

A287940 a(n) is the first odd prime greater than a(n-1) such that (a(1), ..., a(n)) forms a prime vector. a(1)=3, a(2)=5.

Original entry on oeis.org

3, 5, 11, 13, 29, 31, 47, 61, 71, 409, 2819, 4261, 113819, 124633, 236507, 250693, 501779, 886609, 29089889, 57721663, 157320827, 465327091, 812828249, 1530361321

Offset: 1

Dmitry Kamenetsky, Jun 03 2017

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.

a(1)-a(24) were found by Herbert Kociemba.

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

Cf. A286263, A287939.

cp's OEIS Frontend

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

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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.

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A287940 a(n) is the first odd prime greater than a(n-1) such that (a(1), ..., a(n)) forms a prime vector. a(1)=3, a(2)=5.

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