A341338 a(n) is the smallest prime that is simultaneously the sum of 2n-1, 2n+1 and 2n+3 consecutive primes.

83, 311, 55813, 437357, 1219789, 8472193, 9496853, 6484103, 2166953, 37296143, 12671599, 13432571, 14968909, 145616561, 732092831, 220872569, 1381099933, 93482633, 4142423, 87030017, 3193060007, 736535783, 6390999871, 280886077, 464341303, 268231657, 686836817, 9000046663

Offset: 1

Author

Zak Seidov, Apr 25 2021

Keywords

• nonn

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

Array[(k=1;
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 *)