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 A253685 #23 Jul 20 2017 23:17:00 %S A253685 3,13,2,1657,2,83,5,431,5,199,3 %N A253685 Primes r with A253683(n) > A253684(n) > r such that (A253683(n), A253684(n), r) is a Wieferich triple. %C A253685 In analogy to a Wieferich pair, a set of three primes p, q, r can be called a 'Wieferich triple' if its members satisfy either of the following two sets of congruences: %C A253685 p^(q-1) == 1 (mod q^2), q^(r-1) == 1 (mod r^2), r^(p-1) == 1 (mod p^2) %C A253685 p^(r-1) == 1 (mod r^2), r^(q-1) == 1 (mod q^2), q^(p-1) == 1 (mod p^2) %C A253685 a(9) must have A253683(n) > 121637. - _Felix Fröhlich_, Jun 18 2016 %C A253685 a(12) must have A253683(n) > 5*10^6. - _Giovanni Resta_, Jun 20 2016 %H A253685 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wieferich_pair">Wieferich pair</a> %o A253685 (PARI) forprime(p=1, , forprime(q=1, p, forprime(r=1, q, if((Mod(p, q^2)^(q-1)==1 && Mod(q, r^2)^(r-1)==1 && Mod(r, p^2)^(p-1)==1) || (Mod(p, r^2)^(r-1)==1 && Mod(r, q^2)^(q-1)==1 && Mod(q, p^2)^(p-1)==1), print1(r, ", "))))) %Y A253685 Cf. A124121, A124122. %Y A253685 Cf. A253683, A253684. %K A253685 nonn,hard,more %O A253685 1,1 %A A253685 _Felix Fröhlich_, Jan 09 2015 %E A253685 a(8) from _Felix Fröhlich_, Jun 18 2016 %E A253685 Name edited by _Felix Fröhlich_, Jun 18 2016 %E A253685 a(9)-a(11) from _Giovanni Resta_, Jun 20 2016