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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000040, A047948, A122535, A293393, A293395.

Sequence in context: A226003 A203921 A237918 * A242142 A117282 A076750

Adjacent sequences:  A294144 A294145 A294146 * A294148 A294149 A294150

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Oct 23 2017

STATUS

approved

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Last modified June 29 15:47 EDT 2022. Contains 354913 sequences. (Running on oeis4.)