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 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). 0

%I

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

%N 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).

%C 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.

%H R. Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/FermQ_Sorg.txt">Thema: Fermatquotient B^(P-1) == 1 (mod P^2)</a>

%o (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++))

%Y Cf. A039951.

%K nonn,hard,more

%O 0,1

%A _Felix Fröhlich_, Apr 02 2015

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Last modified January 20 14:26 EST 2020. Contains 331094 sequences. (Running on oeis4.)