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 A298763 #20 Sep 03 2020 15:09:40
%S A298763 19,29,1303,3119,4933,6353,7841,10859,13933,24749,26513,28603,31069,
%T A298763 33487,38609,43067,52387,53731,61979,78031,91781,93871,97561,102929,
%U A298763 108127,112403,113341,114599,141937,144967,151883,151969,192883,224909,267961,270371,270577,270763,281531,282959,285979
%N A298763 Numbers that are the smallest of four consecutive primes, no three of which sum to a nonprime.
%H A298763 Hans Havermann, <a href="/A298763/b298763.txt">Table of n, a(n) for n = 1..10000</a>
%e A298763 19, 23, 29, 31 are four consecutive primes. The four ways of adding three of them yields 71, 73, 79, 83, all of which are prime. So 19 is a term of the sequence.
%t A298763 s={2,3,5,7}; p=s[[-1]]; While[p<10^6, If[PrimeQ[s[[1]]+s[[2]]+s[[3]]]&&PrimeQ[s[[1]]+s[[2]]+s[[4]]]&&PrimeQ[s[[1]]+s[[3]]+s[[4]]]&&PrimeQ[s[[2]]+s[[3]]+s[[4]]], Print[s[[1]]]]; p=NextPrime[p]; s=Join[Rest[s],{p}]]
%Y A298763 Subsequence of A073681.
%K A298763 nonn
%O A298763 1,1
%A A298763 _Hans Havermann_, Jan 26 2018