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Second base-n Wieferich prime, i.e., second smallest prime p such that n^(p-1) == 1 (mod p^2).
1

%I #4 Feb 07 2016 20:18:44

%S 3511,1006003,3511,20771,534851,491531,1093,11,487

%N Second base-n Wieferich prime, i.e., second smallest prime p such that n^(p-1) == 1 (mod p^2).

%C Column 2 of table T(n, k) of k-th base-n Wieferich prime for n > 1 (that table is not yet in the OEIS as a sequence).

%C a(11) is unknown, but must be larger than 1.202*10^13 if it exists (cf. Fischer).

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

%e a(3) = 1006003, because 1006003 is the second smallest prime p satisfying 3^(p-1) == 1 (mod p^2) (see A014127).

%o (PARI) a(n) = my(i=0); forprime(p=1, , if(Mod(n, p^2)^(p-1)==1, if(i > 0, return(p), i++)))

%Y Cf. A039951, A178871.

%K nonn,hard,more

%O 2,1

%A _Felix Fröhlich_, Feb 02 2016