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A124122
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Least prime p such that (p,q) is a Double Wieferich prime pair for q=A124121(n).
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4
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OFFSET
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1,1
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COMMENTS
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Double Wieferich prime pairs are pairs of primes (p, q) such that q^(p-1) == 1 (mod p^2) and p^(q-1) == 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
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LINKS
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Table of n, a(n) for n=1..6.
Y. F. Bilu, Catalan's Conjecture.
Michael Mossinghoff, Wieferich Prime Pairs, Barker Sequences, and Circulant Hadamard Matrices, as of Feb 12 2009.
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PROG
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(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)^(q-1)-1 & next; Mod(q, p^2)^(p-1)-1 | print1( p", ") | break)) \\ M. F. Hasler, Oct 08 2011
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CROSSREFS
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See A124121 for values of q.
Cf. A196511, A196733.
Sequence in context: A115192 A091674 A022197 * A163561 A203807 A184470
Adjacent sequences: A124119 A124120 A124121 * A124123 A124124 A124125
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KEYWORD
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nonn,hard,more
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AUTHOR
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N. J. A. Sloane, following an email from Robert G. Wilson v, Nov 30 2006
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STATUS
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approved
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