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%I #11 Oct 25 2017 17:15:35
%S 3,71,7,463,31,43,5,7,499,821,109,97,271,263,179,97,181,47,233,1931,
%T 359,227,1787,443,29,131,1061,229,599,1931,7,317,53,2207,811,11549,
%U 2411,2879,5531,937,2371,293,21001,659,643,1187,2927,4567,131,263,8419,349
%N a(n) = the first prime in the earliest sequence of 2n+1 consecutive primes whose average is prime.
%e 71 is the first prime in the earliest sequence of 5 = 2 * 2 + 1 consecutive primes whose average is a prime, since (71 + 73 + 79 + 83 + 89)/5 = 79. Therefore a(2) = 71.
%t f[n_] := Block[{k = 1}, While[ !PrimeQ[ Sum[ Prime[j], {j, k, 2n + k}]/(2n + 1)], k++ ]; Prime[k]]; Table[ f[n], {n, 52}] (* _Robert G. Wilson v_, Jun 21 2005 *)
%t Module[{prs=Prime[Range[25000]]},Table[SelectFirst[Partition[ prs,2n+1,1], PrimeQ[ Mean[ #]]&],{n,60}]][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 25 2017 *)
%K nonn
%O 1,1
%A _Joseph L. Pe_, Jun 16 2005
%E More terms from _Robert G. Wilson v_, Jun 21 2005
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