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

Author

N. J. A. Sloane, Jan 25 2006

Keywords

• nonn
• tabf

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}.

Examples

			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}.
		

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

Crossrefs

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

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

Extensions

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