A317678 -id:A317678 - cp's OEIS frontend

A317679 Sets of n distinct primes q_i in ascending order, written as a triangle, providing the fair compensation amounts corresponding to the asset counts p_i of A317678.

1, 5, 23, 7, 31, 103, 7, 17, 47, 67, 7, 31, 43, 103, 211, 19, 47, 61, 89, 131, 313, 7, 23, 103, 167, 263, 359, 503, 47, 83, 101, 137, 191, 353, 461, 587, 13, 53, 73, 113, 173, 193, 293, 353, 953, 7, 29, 73, 139, 227, 293, 557, 601, 821, 1063

Offset: 1

Hugo Pfoertner, Aug 10 2018

See A317678 for detailed information. Since there is no solution satisfying the criteria for n=1, a(1)=1 is set to complete the triangle.

			Triangle begins:
   1;
   5, 23;
   7, 31, 103;
   7, 17,  47,  67;
   7, 31,  43, 103, 211;
  19, 47,  61,  89, 131, 313;
   7, 23, 103, 167, 263, 359, 503;
   ...

Cf. A317678, A317680.

A317680 Least sum S_n of n distinct primes p_i such that q_j = np_j - Sum_{k=1..n,k!=j} p_k, j=1..n is prime, such that the set union {p_i} U {q_i} contains 2n distinct primes.

Original entry on oeis.org

28, 141, 138, 395, 660, 1425, 1960, 2217, 3810, 5005, 7230

Offset: 2

Hugo Pfoertner, Aug 10 2018

The sets of primes p_i and q_i and a description of the problem are provided in A317678 and A317679. a(1) is omitted to indicate the nonexistence of a solution.

a(13) <= 8955, a(14) <= 12122.

Cf. A317678, A317679.

cp's OEIS Frontend

A317679 Sets of n distinct primes q_i in ascending order, written as a triangle, providing the fair compensation amounts corresponding to the asset counts p_i of A317678.

Views

Author

Keywords

Comments

Examples

Crossrefs

A317680 Least sum S_n of n distinct primes p_i such that q_j = np_j - Sum_{k=1..n,k!=j} p_k, j=1..n is prime, such that the set union {p_i} U {q_i} contains 2n distinct primes.

Views

Author

Keywords

Comments

Crossrefs

cp's OEIS Frontend

A317679 Sets of n distinct primes q_i in ascending order, written as a triangle, providing the fair compensation amounts corresponding to the asset counts p_i of A317678.

Views

Author

Keywords

Comments

Examples

Crossrefs

A317680 Least sum S_n of n distinct primes p_i such that q_j = n*p_j - Sum_{k=1..n,k!=j} p_k, j=1..n is prime, such that the set union {p_i} U {q_i} contains 2*n distinct primes.

Views

Author

Keywords

Comments

Crossrefs

A317680 Least sum S_n of n distinct primes p_i such that q_j = np_j - Sum_{k=1..n,k!=j} p_k, j=1..n is prime, such that the set union {p_i} U {q_i} contains 2n distinct primes.