%N Primes p where A196202 reaches a new local minimum, i.e., the value of A196202 is strictly smaller than the value for both the previous prime and the next prime.
%C A Wieferich prime p (A001220) is in this sequence iff neither A000040(i-1) nor A000040(i+1) is a Wieferich prime, where i is the index of p in A000040.
%C Conjecture: There are no consecutive Wieferich primes, i.e., A001220 is a subsequence of this sequence.
%C The truth of the previous conjecture would follow from the truth of the heuristic assumption that there are about log(log(x)) Wieferich primes below x for large x.
%o (PARI) a196202(n) = lift(Mod(2, n^2)^(n-1))
%o is(n) = (ispseudoprime(n)) && (a196202(n) < a196202(precprime(n-1))) && (a196202(n) < a196202(nextprime(n+1)))
%Y Cf. A000040, A001220, A196202.
%A _Felix Fröhlich_, May 27 2017