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%I #18 Mar 19 2016 14:05:51
%S 3,7,3,7,19,3,11,23,71,5,29,53,89,113,3,11,83,131,251,383,5,29,113,
%T 269,353,449,509,5,17,41,101,257,521,761,881,23,431,503,683,863,1091,
%U 1523,1871,2963,31,1123,1471,1723,3463,3571,4651,5563,5743,6991
%N 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.
%C If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.
%C For distinct primes, the solution for n=5 is {5, 29, 53, 89, 173}.
%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 Toshitaka Suzuki, <a href="/A113832/b113832.txt">Table of n, a(n) for n = 2..91</a>
%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 3, 7, 19
%e 3, 11, 23, 71
%e 5, 29, 53, 89, 113
%e 3, 11, 83, 131, 251, 383
%e 5, 29, 113, 269, 353, 449, 509
%e The set of primes generated by {5, 29, 53, 89, 113} is {17, 29, 41, 47, 59, 59, 71, 71, 83, 101}.
%Y Cf. A113827-A113831, A113833, A113834, A088430.
%Y See A115631 for the case when all pairwise averages are distinct primes.
%K nonn,tabf
%O 2,1
%A _N. J. A. Sloane_, Jan 25 2006
%E More terms from _T. D. Noe_, Feb 01 2006
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