|
|
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).
|
|
9
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Does b exist for all n?
|
|
LINKS
|
|
|
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 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|