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 A224695 #16 Jul 12 2019 17:55:16 %S A224695 561,645,1905,2465,4369,4371,23001,25761,60701,87249,158369,181901, %T A224695 206601,212421,253241,280601,332949,348161,513629,580337,587861, %U A224695 656601,831405,1207361,1275681,1472505,1489665,1678541,1735841,1815465,1909001,2113665,2290641,2419385 %N A224695 Pseudoprimes to a twin prime criterion of Aebi and Cairns. %C A224695 Theorem 3 in the paper (see link) states that if p and p+2 are both prime then 2^(p+2) == 3*p+8 mod p(p+2). This sequence lists the pseudoprimes to this criterion. %C A224695 Of the first 27 terms listed, 16 are divisible by 3. %H A224695 Amiram Eldar, <a href="/A224695/b224695.txt">Table of n, a(n) for n = 1..903</a> (terms below 10^11) %H A224695 Christian Aebi and Grant Cairns, <a href="http://dx.doi.org/10.4171/EM/103">Catalan numbers, primes and twin primes</a>, Elemente der Mathematik, Vol. 63, No. 4 (2008), pp. 153-164. %p A224695 for n from 1 to 1500000 do if 2^(n+2) mod n*(n+2)=3*n+8 and not isprime(n) then print(n) fi od; %t A224695 aQ[n_] := CompositeQ[n] && PowerMod[2, n + 2, n*(n + 2)] == 3*n + 8; Select[ %t A224695 Range[10^6], aQ] (* _Amiram Eldar_, Jul 12 2019 *) %o A224695 (PARI) isok(n) = (n>1) && !isprime(n) && Mod(2, n*(n+2))^(n+2) == Mod(3*n+8, n*(n+2)); \\ _Michel Marcus_, Jul 12 2019 %K A224695 nonn %O A224695 1,1 %A A224695 _Gary Detlefs_, Apr 15 2013 %E A224695 a(14) and more terms from _Amiram Eldar_, Jul 12 2019