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 A287217 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. 0

%I

%S 7,13,19,29,37,59,71,79,89,107,131,139,151,173,191,211,233,263,277,

%T 283,313,331,359,379,389,409,439,467,491,503,521,541,569,587,599,613,

%U 647,659,677,691,739,757,773,809,823,839,857,863,881,929,941,953,977,991

%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.

%K nonn

%O 1,1

%A _Felix Fröhlich_, May 27 2017

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Last modified May 27 12:49 EDT 2022. Contains 354097 sequences. (Running on oeis4.)