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.

2, 83, 2903, 911, 3, 5

Offset: 1

Author

Felix Fröhlich, Aug 05 2018

Keywords

• nonn
• hard
• more

Examples

			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).
		

Links

• Eric Weisstein's World of Mathematics, Double Wieferich Prime Pair

Crossrefs

Cf. A266829. Supersequence of A124121.

Cf. A282293.

Programs

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)))