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

11, 23, 5, 1667, 73, 821, 18043, 2393, 20771, 2251, 1006003

Offset

1,1

Comments

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:

p^(q-1) == 1 (mod q^2), q^(r-1) == 1 (mod r^2), r^(p-1) == 1 (mod p^2)

p^(r-1) == 1 (mod r^2), r^(q-1) == 1 (mod q^2), q^(p-1) == 1 (mod p^2)

a(9) must have A253683(n) > 121637. - Felix Fröhlich, Jun 18 2016

a(12) must have A253683(n) > 5*10^6. - Giovanni Resta, Jun 20 2016

Links

Table of n, a(n) for n=1..11.

Wikipedia, Wieferich pair

Prog

(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, ", ")))))

Crossrefs

Cf. A124121, A124122.

Cf. A253683, A253685.

Sequence in context: A225186 A155973 A351849 * A364165 A180481 A110044

Adjacent sequences: A253681 A253682 A253683 * A253685 A253686 A253687

Keyword

nonn,hard,more

Author

Felix Fröhlich, Jan 09 2015

Extensions

a(8) from Felix Fröhlich, Jun 18 2016

Name edited by Felix Fröhlich, Jun 18 2016

a(9)-a(11) from Giovanni Resta, Jun 20 2016

Status

approved