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%I #16 Jun 18 2021 15:07:34
%S 3,7,7,19,67,5,17,89,1277,209173,322573,536773,1217893,2484733
%N 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.
%C If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.
%C 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
%D 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]
%H Jens Kruse Andersen, <a href="http://primerecords.dk/aprecords.htm">Primes in Arithmetic Progression Records</a> [May have candidates for later terms in this sequence.]
%H Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePatterns.pdf">Prime number patterns</a>
%e Triangle begins:
%e 3, 7
%e 7, 19, 67
%e 5, 17, 89, 1277
%Y Cf. A113827-A113831, A113832, A113834, A088430.
%K nonn,tabf,more
%O 2,1
%A _N. J. A. Sloane_, Jan 25 2006
%E Row 5 from _T. D. Noe_, Aug 08 2006