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 A154501 #4 Jun 19 2021 12:50:00
%S A154501 3,11,17,31,41,59,97,113,127,139
%N A154501 Sum of any 3 consecutive numbers is prime and a(n+2)-(a(n+1)+a(n)) is prime, a(1)=3,a(2)=11.
%C A154501 3+11+17=31;17-(3+11)=3,...
%t A154501 a=3;b=11;lst={a,b};Do[c=Prime[n];p1=c+a+b;p2=c-(a+b);If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,c];a=b;b=c],{n,5,9!}];lst
%Y A154501 Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497, A154498, A154500
%K A154501 nonn
%O A154501 1,1
%A A154501 _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009
%E A154501 NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021