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 A153406 #6 Oct 25 2020 15:05:26
%S A153406 4813,9007,13831,33791,35023,48337,51577,52153,61297,62207,77743,
%T A153406 95107,102607,105137,105673,109663,111767,114781,119747,128221,135367,
%U A153406 136727,138679,149197,153949,159787,163199,165437,174829,188677,195973,208009
%N A153406 Smallest of 3 consecutive prime numbers such that p1*p2*p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.
%C A153406 4813*4817*4831+4+14=112002971670+-1=primes,...
%H A153406 Harvey P. Dale, <a href="/A153406/b153406.txt">Table of n, a(n) for n = 1..1000</a>
%t A153406 lst={};Do[p1=Prime[n];p2=Prime[n+1];p3=Prime[n+2];d1=p2-p1;d2=p3-p2;a=p1*p2*p3+d1+d2+1;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p1]],{n,8!}];lst
%t A153406 s3cpnQ[n_]:=Module[{c=Times@@n+Total[Differences[n]]+1},AllTrue[c+{1,-1}, PrimeQ]]; Transpose[Select[Partition[ Prime[Range[ 20000]],3,1], s3cpnQ]] [[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 05 2014 *)
%Y A153406 Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405
%K A153406 nonn
%O A153406 1,1
%A A153406 _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008