This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370139 #31 Feb 12 2024 15:00:21
%S A370139 19,29,31,53,79,379,401,839,883,1301,1409,1951,1973,2113,2683,2791,
%T A370139 2833,3407,3613,3793,3823,4441,4751,4831,5623,5827,6133,6329,7187,
%U A370139 7237,7703,8527,9173,10103,10853,11317,12277,13163,13933,14159,14827,15241,15667
%N A370139 Primes p such that the sums of three, five, and seven consecutive primes starting with p are prime.
%H A370139 Harvey P. Dale, <a href="/A370139/b370139.txt">Table of n, a(n) for n = 1..1000</a>
%e A370139 379 is in the sequence because the seven consecutive primes starting with 379 are 379, 383, 389, 397, 401, 409, and 419, and (379+383+389)=1151, and (379+383+389+397+401)=1949, and (379+383+389+397+401+409+419)=2777, and 1151 and 1949 and 2777 are all primes.
%t A370139 Select[Partition[Prime[Range[5000]],7,1],AllTrue[{Total[Take[#,3]],Total[Take[#,5]],Total[#]},PrimeQ]&][[;;,1]]
%Y A370139 Intersection of A180948 and A182121.
%K A370139 nonn
%O A370139 1,1
%A A370139 _Harvey P. Dale_, Feb 11 2024