A256565 Smallest base b > 1 such that the smallest base-b Wieferich prime p (i.e., prime p satisfying b^(p-1) == 1 mod (p^2)) lies between 10^n and 10^(n+1).

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

Offset

0,1

Comments

In other words, the smallest base b where the smallest base-b 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^(P-1) == 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)^(p-1)==1, badwief++; break({1}))); if(badwief==0, forprime(p=10^n, 10^(n+1), if(Mod(b, p^2)^(p-1)==1, print1(b, ", "); goodwief++; break({1})))); b++))

Crossrefs

Cf. A039951.

Sequence in context: A092525 A101367 A338790 * A298098 A248256 A369039

Adjacent sequences: A256562 A256563 A256564 * A256566 A256567 A256568

Keyword

nonn,hard,more

Author

Felix Fröhlich, Apr 02 2015

Status

approved