A115631 -id:A115631 - cp's OEIS frontend

A155463 Largest element of a set of n primes with the property that the pairwise averages are all distinct primes, having the smallest largest element (A115631).

7, 19, 71, 173, 383, 881, 2111, 5417, 10691, 21757, 27611

Offset: 2

Dmitry Kamenetsky, Jan 22 2009

nonn

The solution for n=5 is {5, 29, 53, 89, 173}, so a(5)=173. This sequence is not proved to be optimal, so smaller terms may exist.

Andrew Granville, Prime number patterns

Cf. A115631, A113832.

A113832 Triangle read by rows: row n (n>=2) gives a set of n primes with the property that the pairwise averages are all primes, having the smallest largest element.

Original entry on oeis.org

3, 7, 3, 7, 19, 3, 11, 23, 71, 5, 29, 53, 89, 113, 3, 11, 83, 131, 251, 383, 5, 29, 113, 269, 353, 449, 509, 5, 17, 41, 101, 257, 521, 761, 881, 23, 431, 503, 683, 863, 1091, 1523, 1871, 2963, 31, 1123, 1471, 1723, 3463, 3571, 4651, 5563, 5743, 6991

Offset: 2

N. J. A. Sloane, Jan 25 2006

If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.

For distinct primes, the solution for n=5 is {5, 29, 53, 89, 173}.

			Triangle begins:
3, 7
3, 7, 19
3, 11, 23, 71
5, 29, 53, 89, 113
3, 11, 83, 131, 251, 383
5, 29, 113, 269, 353, 449, 509
The set of primes generated by {5, 29, 53, 89, 113} is {17, 29, 41, 47, 59, 59, 71, 71, 83, 101}.

Antal Balog, The prime k-tuplets conjecture on average, in "Analytic Number Theory" (eds. B. C. Berndt et al.) Birkhäuser, Boston, 1990, pp. 165-204. [Background]

Toshitaka Suzuki, Table of n, a(n) for n = 2..91
Jens Kruse Andersen, Primes in Arithmetic Progression Records [May have candidates for later terms in this sequence.]
Andrew Granville, Prime number patterns

Cf. A113827-A113831, A113833, A113834, A088430.

See A115631 for the case when all pairwise averages are distinct primes.

More terms from T. D. Noe, Feb 01 2006

cp's OEIS Frontend

A155463 Largest element of a set of n primes with the property that the pairwise averages are all distinct primes, having the smallest largest element (A115631).

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