

A124122


Least prime p such that (p,q) is a Double Wieferich prime pair for q=A124121(n).


12




OFFSET

1,1


COMMENTS

Double Wieferich prime pairs are pairs of primes (p, q) such that q^(p1) == 1 (mod p^2) and p^(q1) == 1 (mod q^2). This sequence gives the (least) value of p corresponding to the q's listed in increasing order (and without multiplicity) in A124121.
This is just the list of known pairs: there may be gaps.
Currently there are two known double Wieferich prime pairs (p, q) with q = 5: (1645333507, 5) and (188748146801, 5).  Alexander Adamchuk, Mar 10 2007


LINKS

Table of n, a(n) for n=1..6.
Y. F. Bilu, Catalan's Conjecture, Séminaire Bourbaki, 45 (20022003), pp. 126.
Michael Mossinghoff, Wieferich Prime Pairs, Barker Sequences, and Circulant Hadamard Matrices, as of Feb 12 2009.
Wikipedia, Wieferich pair


PROG

(PARI) /* The following (highly unoptimized) code misses the value a(3) but prints all other values in less than 30 seconds. */
default(primelimit, 1010000); forprime(q=1, default(primelimit), forprime(p=q+1, default(primelimit), Mod(p, q^2)^(q1)1 & next; Mod(q, p^2)^(p1)1  print1( p", ")  break)) \\ M. F. Hasler, Oct 08 2011
(PARI) a(n) = my(q=prime(n), p=2); while(Mod(p, q^2)^(q1)!=1  Mod(q, p^2)^(p1)!=1, p=nextprime(p+1)); p \\ Felix Fröhlich, Jan 04 2016


CROSSREFS

See A124121 for values of q.
Cf. A196511, A196733.
Sequence in context: A091674 A022197 A259909 * A163561 A203807 A184470
Adjacent sequences: A124119 A124120 A124121 * A124123 A124124 A124125


KEYWORD

nonn,hard,more


AUTHOR

N. J. A. Sloane, following an email from Robert G. Wilson v, Nov 30 2006


STATUS

approved



