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%I #11 Nov 09 2017 14:06:51
%S 63487,462067,830777,847507,1012159,1049773,1250611,1268747,1372537,
%T 1372559,1589657,1988237,2567557,2696569,2874673,2967317,3676111,
%U 3718657,4196987,4255067,4550867,4669333,5217911,5225147,5716031,6019553,6103171,6725657,6725731,7143557
%N Initial member of 9 consecutive primes {a, b, c, d, e, f, g, h, i} such that (a + b + c)/3, (d + e + f)/3 and (g + h + i)/3 are all prime.
%e 63487 is a term because it is the initial term of 9 consecutive primes {63487, 63493, 63499, 63521, 63527, 63533, 63541, 63559, 63577} = {a, b, c, d, e, f, g, h, i}: the arithmetic mean of three sets, i.e., (a + b + c)/ 3, (d + e + f)/3 and (g + h + i)/3 is prime.
%t Select[Partition[Prime@ Range[5*10^5], 9, 1], Function[{a, b, c, d, e, f, g, h, i}, AllTrue[{(a + b + c)/3, (d + e + f)/3, (g + h + i)/3}, PrimeQ]] @@ # &][[All, 1]] (* _Michael De Vlieger_, Oct 23 2017 *)
%Y Cf. A000040, A047948, A122535, A293393, A293395.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Oct 23 2017