This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259075 #21 Jul 07 2015 14:18:42
%S A259075 17,26,18,148,239,249,423,28,63,374,117,787,2059,1085,655,4586,4153,
%T A259075 3147,10056,4559,2092,18692,19487,3018,19343,14285,164,31469,6817,
%U A259075 7916,16128,4505,18768,2752,26664,16717,129702,46171,1040,3608,9479,4840,42348,14128
%N 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).
%C A259075 Does b exist for all n?
%C A259075 a(n) == A039678(n) iff A039678(n) == A039678(n+1). The smallest n where those equalities hold is n = 8.
%H A259075 Felix Fröhlich, <a href="/A259075/b259075.txt">Table of n, a(n) for n = 1..1000</a>
%t A259075 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 *)
%o A259075 (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
%Y A259075 Cf. A039678.
%K A259075 nonn
%O A259075 1,1
%A A259075 _Felix Fröhlich_, Jun 18 2015