cp's OEIS Frontend

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.

A253684 Primes q with A253683(n) > q > A253685(n) such that (A253683(n), q, A253685(n)) forms a Wieferich triple.

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%I A253684 #23 Jul 20 2017 23:16:49
%S A253684 11,23,5,1667,73,821,18043,2393,20771,2251,1006003
%N A253684 Primes q with A253683(n) > q > A253685(n) such that (A253683(n), q, A253685(n)) forms a Wieferich triple.
%C A253684 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 A253684 p^(q-1) == 1 (mod q^2), q^(r-1) == 1 (mod r^2), r^(p-1) == 1 (mod p^2)
%C A253684 p^(r-1) == 1 (mod r^2), r^(q-1) == 1 (mod q^2), q^(p-1) == 1 (mod p^2)
%C A253684 a(9) must have A253683(n) > 121637. - _Felix Fröhlich_, Jun 18 2016
%C A253684 a(12) must have A253683(n) > 5*10^6. - _Giovanni Resta_, Jun 20 2016
%H A253684 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wieferich_pair">Wieferich pair</a>
%o A253684 (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(q, ", ")))))
%Y A253684 Cf. A124121, A124122.
%Y A253684 Cf. A253683, A253685.
%K A253684 nonn,hard,more
%O A253684 1,1
%A A253684 _Felix Fröhlich_, Jan 09 2015
%E A253684 a(8) from _Felix Fröhlich_, Jun 18 2016
%E A253684 Name edited by _Felix Fröhlich_, Jun 18 2016
%E A253684 a(9)-a(11) from _Giovanni Resta_, Jun 20 2016