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 A154496 #4 Jun 19 2021 12:52:27
%S A154496 3,10,27,74,3093,3104,3417,3580,3597,3614,5907,5960,6651,6962,9045,
%T A154496 9098,10479,10708,13299,13382,14055,14438,15099,16082,16101,16112,
%U A154496 16521,16982,17505,19328,19605,20062,22131,22840,23013,23036,23265,23422
%N A154496 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=3,a(2)=10.
%C A154496 Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 10-3=7;10+3=13;10*3=30, ...
%t A154496 a=3;b=10;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1],AppendTo[lst,n];a=b;b=n],{n,b+1,9!}];lst
%Y A154496 Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495
%K A154496 nonn
%O A154496 1,1
%A A154496 _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009
%E A154496 NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021