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 A154484 #6 Apr 20 2022 14:12:57
%S A154484 0,2,5,8,11,18,23,30,37,42,47,50,53,56,75,82,85,88,91,102,109,114,119,
%T A154484 122,129,134,137,140,143,150,157,160,171,176,183,190,193,196,201,208,
%U A154484 211,222,227,230,233,246,253,256,267,274,297,302,305,308,311,330,343
%N A154484 a(n+1)-+a(n) = prime, a(1)=0, a(2)=2.
%C A154484 Sum and difference of any of two consecutive numbers are prime numbers: 5-2=3; 5+2=7, 230-227=3; 230+227=457, 233-230=3; 233+230=463,...
%C A154484 I assume that here and in most of the similar sequences from the same author there is an implicit assumption that we want the "Lexicographically earliest infinite sequence of distinct positive numbers" that satisfies the stated condition. - _N. J. A. Sloane_, Apr 20 2022
%t A154484 a=0;b=2;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b],AppendTo[lst,n];a=b;b=n],{n,3,7!}];lst
%K A154484 nonn
%O A154484 1,2
%A A154484 _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009
%E A154484 NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021