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A317724 Smallest prime q < A266829(n) such that both A266829(n)^(q-1) == 1 (mod q^2) and q^(A266829(n)-1) == 1 (mod A266829(n)^2), i.e., smallest prime q less than A266829(n) such that q and A266829(n) form a double Wieferich prime pair. 1

%I #10 Feb 20 2019 21:42:51

%S 2,83,2903,911,3,5

%N Smallest prime q < A266829(n) such that both A266829(n)^(q-1) == 1 (mod q^2) and q^(A266829(n)-1) == 1 (mod A266829(n)^2), i.e., smallest prime q less than A266829(n) such that q and A266829(n) form a double Wieferich prime pair.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DoubleWieferichPrimePair.html">Double Wieferich Prime Pair</a>

%e a(2) = 83, because 83 is the smallest prime q such that A266829(2) = 4871 satisfies both 4871^(q-1) == 1 (mod q^2) and q^(4871-1) == 1 (mod 4871^2).

%o (PARI) forprime(p=3, , forprime(q=2, p-1, if(Mod(p, q^2)^(q-1)==1 && Mod(q, p^2)^(p-1)==1, print1(q, ", "); break)))

%Y Cf. A266829. Supersequence of A124121.

%Y Cf. A282293.

%K nonn,hard,more

%O 1,1

%A _Felix Fröhlich_, Aug 05 2018

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