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 A153404 #7 Dec 22 2019 08:04:42
%S A153404 5,571,1753,5113,6949,9283,11047,14401,24859,25171,26203,31159,34471,
%T A153404 41719,42397,45289,61099,62533,80611,82141,90001,91969,92347,93811,
%U A153404 98377,98887,103591,105907,111373,117133,120997,122827,128413,135607
%N A153404 Middle 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.
%H A153404 Amiram Eldar, <a href="/A153404/b153404.txt">Table of n, a(n) for n = 1..10000</a>
%e A153404 3*5*7 + 2 + 2 - 1 = 108 and 108 +- 1 are primes.
%t A153404 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,p2]],{n,8!}];lst
%Y A153404 Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402.
%K A153404 nonn
%O A153404 1,1
%A A153404 _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008