

A256565


Smallest base b > 1 such that the smallest baseb Wieferich prime p (i.e., prime p satisfying b^(p1) == 1 mod (p^2)) lies between 10^n and 10^(n+1).


0



5, 3, 20, 2, 6, 142, 183, 66, 294, 88, 34, 387
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OFFSET

0,1


COMMENTS

In other words, the smallest base b where the smallest baseb Wieferich prime has exactly n+1 digits; i.e., a(n) is the smallest b > 1 such that A055642(A039951(b)) = n+1.


LINKS

Table of n, a(n) for n=0..11.
R. Fischer, Thema: Fermatquotient B^(P1) == 1 (mod P^2)


PROG

(PARI) for(n=0, 20, b=2; goodwief=0; while(goodwief==0, badwief=0; forprime(p=1, 10^n, if(Mod(b, p^2)^(p1)==1, badwief++; break({1}))); if(badwief==0, forprime(p=10^n, 10^(n+1), if(Mod(b, p^2)^(p1)==1, print1(b, ", "); goodwief++; break({1})))); b++))


CROSSREFS

Cf. A039951.
Sequence in context: A169697 A092525 A101367 * A298098 A248256 A049457
Adjacent sequences: A256562 A256563 A256564 * A256566 A256567 A256568


KEYWORD

nonn,hard,more


AUTHOR

Felix FrÃ¶hlich, Apr 02 2015


STATUS

approved



