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.

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

2,1

Comments

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}.

References

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]

Links

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

Example

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}.

Crossrefs

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

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

Sequence in context: A320831 A120124 A151573 * A115631 A053008 A053010

Adjacent sequences: A113829 A113830 A113831 * A113833 A113834 A113835

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 25 2006

Extensions

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

Status

approved