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a(n) is the smallest prime that is simultaneously the sum of 2n-1, 2n+1 and 2n+3 consecutive primes.
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%I #16 May 01 2021 22:20:54

%S 83,311,55813,437357,1219789,8472193,9496853,6484103,2166953,37296143,

%T 12671599,13432571,14968909,145616561,732092831,220872569,1381099933,

%U 93482633,4142423,87030017,3193060007,736535783,6390999871,280886077,464341303,268231657,686836817,9000046663

%N a(n) is the smallest prime that is simultaneously the sum of 2n-1, 2n+1 and 2n+3 consecutive primes.

%e For n = 1: 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23, and 83 is the smallest prime that is the sum of 1, 3 and 5 consecutive primes, so a(1) = 83.

%t Array[(k=1;

%t While[(i=Select[Intersection@@((Total/@Subsequences[Prime@Range@Prime[k++],{#}])&/@{2#-1,2#+1,2#+3}),PrimeQ])=={}];First@i)&,4] (* _Giorgos Kalogeropoulos_, Apr 26 2021 *)

%Y Cf. A034962, A034965, A082246, A082251, A127340, A127341, A161612.

%K nonn

%O 1,1

%A _Zak Seidov_, Apr 25 2021