A294147 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.
63487, 462067, 830777, 847507, 1012159, 1049773, 1250611, 1268747, 1372537, 1372559, 1589657, 1988237, 2567557, 2696569, 2874673, 2967317, 3676111, 3718657, 4196987, 4255067, 4550867, 4669333, 5217911, 5225147, 5716031, 6019553, 6103171, 6725657, 6725731, 7143557
Offset: 1
Keywords
Examples
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.
Programs
-
Mathematica
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 *)