%I #17 Feb 24 2024 01:07:53

%S 2,5,5,17,3,5,29,3,3,11,7,7,5,7,13,13,7,5,5,13,7,7,7,7,11,17,3,3,97,

%T 29,3,13,3,19,19,3,5,3,23,7,11,53,31,89,53,19,11,3,17,23,83,11,5,47,

%U 37,5,17,3,3,29,23,5,5,5,59,7,7,31,3,67,3,3,89,71,31

%N a(n) = the first prime in the earliest chain of 2n+1 consecutive primes whose sum is prime.

%C In general (except possibly when it begins with 2), the sum of an even number of consecutive primes is even - hence the restriction to odd chain lengths.

%H T. D. Noe, <a href="/A089793/b089793.txt">Table of n, a(n) for n = 0..10000</a>

%e 17 is the first prime in the chain 17, 19, 23, 29, 31, 37, 41, which is the earliest chain of 2 * 3 + 1 = 7 consecutive primes whose sum, 197, is prime. Hence a(3) = 17.

%t With[{prs=Prime[Range[1000]]},First[#]&/@Flatten[Table[Select[ Partition[ prs,2n+1,1],PrimeQ[Total[#]]&,1],{n,0,80}],1]] (* _Harvey P. Dale_, Jun 21 2013 *)

%Y Cf. A070934, A215235, A180950, A226380.

%K nonn

%O 0,1

%A _Joseph L. Pe_, Jan 09 2004