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 A154493 #4 Jun 19 2021 12:53:57
%S A154493 1,4,15,28,39,50,81,350,459,512,675,944,987,1040,1917,1936,2325,2378,
%T A154493 2421,2588,2745,2812,3459,3488,3495,3506,5667,5804,6027,6074,24765,
%U A154493 24832,25479,25552,27621,27848,27951,27980,34101,34720,34773,35344
%N A154493 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=1,a(2)=4.
%C A154493 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 : 4-1=3;4+1=5;4*1=4, 15-4=11;15+4=19;15*4=60, ...
%t A154493 a=1;b=4;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 A154493 Cf. A154484, A154485, A154486, A154487, A154488
%K A154493 nonn
%O A154493 1,2
%A A154493 _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009
%E A154493 NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021