A289379 - OEIS

A289379

Primes p that set a new record for the size of the smallest prime q such that q^(p-1) == 1 (mod p^2), i.e., such that p is a base-q Wieferich prime.

%I #32 Sep 04 2017 23:19:48

%S 2,3,7,17,23,37,67,89,139,163,269,379,439,491,691,701,877,1009,1327,

%T 1427,1669,2687,4973,6367,7603,9277,10531,11047,12071,18313,29389,

%U 34471,42703,42961,57731,77773,87299,105517,113957,118369,151303,192631,205603,232091

%N Primes p that set a new record for the size of the smallest prime q such that q^(p-1) == 1 (mod p^2), i.e., such that p is a base-q Wieferich prime.

%C For n > 1, primes p such that A125636(i) reaches record values, where i is the index of p in A000040.

%o (PARI) minprimb(n) = forprime(q=1, , if(Mod(q, n^2)^(n-1)==1, return(q)))

%o my(r=0); forprime(p=1, , if(minprimb(p) > r, print1(p, ", "); r=minprimb(p)))

%Y Cf. A000040, A125636, A287147.

%K nonn

%O 1,1

%A _Felix Fröhlich_, Sep 02 2017

%E a(37)-a(44) from _Giovanni Resta_, Sep 02 2017