A113833 Triangle read by rows: row n (n>=2) gives a set of n primes such that the averages of all subsets are distinct primes, having the smallest largest element.

3, 7, 7, 19, 67, 5, 17, 89, 1277, 209173, 322573, 536773, 1217893, 2484733

Offset

2,1

Comments

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

Note that, in each row, the n primes are equal modulo 4, 12, 12 and 120, respectively. - Row 5 from T. D. Noe, Aug 08 2006

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

Table of n, a(n) for n=2..15.

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
7, 19, 67
5, 17, 89, 1277

Crossrefs

Cf. A113827-A113831, A113832, A113834, A088430.

Sequence in context: A229521 A263337 A160994 * A212286 A157102 A226512

Adjacent sequences: A113830 A113831 A113832 * A113834 A113835 A113836

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Jan 25 2006

Extensions

Row 5 from T. D. Noe, Aug 08 2006

Status

approved