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

Author

N. J. A. Sloane, Jan 25 2006

Keywords

• nonn
• tabf
• more

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

Examples

			Triangle begins:
3, 7
7, 19, 67
5, 17, 89, 1277
		

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

• 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, A113832, A113834, A088430.

Extensions

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