A259075 Smallest base b > 1 such that both prime(n) and prime(n+1) are base-b Wieferich primes, i.e., p = prime(n) satisfies b^(p-1) == 1 (mod p^2) and q = prime(n+1) satisfies b^(q-1) == 1 (mod q^2).

17, 26, 18, 148, 239, 249, 423, 28, 63, 374, 117, 787, 2059, 1085, 655, 4586, 4153, 3147, 10056, 4559, 2092, 18692, 19487, 3018, 19343, 14285, 164, 31469, 6817, 7916, 16128, 4505, 18768, 2752, 26664, 16717, 129702, 46171, 1040, 3608, 9479, 4840, 42348, 14128

Offset: 1

Author

Felix Fröhlich, Jun 18 2015

Keywords

• nonn

Comments

Does b exist for all n?

a(n) == A039678(n) iff A039678(n) == A039678(n+1). The smallest n where those equalities hold is n = 8.

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A039678.

Programs

Mathematica

a[n_] := Block[{b=2, p = Prime@{n, n+1}}, While[{1,1} != PowerMod[ b, p-1, p^2], b++]; b]; Array[a, 40] (* Giovanni Resta, Jun 23 2015 *)

PARI

a(n) = p=prime(n); q=prime(n+1); b=2; while(Mod(b, p^2)^(p-1)!=1 || Mod(b, q^2)^(q-1)!=1, b++); b