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.

7, 13, 19, 29, 37, 59, 71, 79, 89, 107, 131, 139, 151, 173, 191, 211, 233, 263, 277, 283, 313, 331, 359, 379, 389, 409, 439, 467, 491, 503, 521, 541, 569, 587, 599, 613, 647, 659, 677, 691, 739, 757, 773, 809, 823, 839, 857, 863, 881, 929, 941, 953, 977, 991

Offset

1,1

Comments

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.

Conjecture: There are no consecutive Wieferich primes, i.e., A001220 is a subsequence of this sequence.

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.

Links

Table of n, a(n) for n=1..54.

Prog

(PARI) a196202(n) = lift(Mod(2, n^2)^(n-1))
is(n) = (ispseudoprime(n)) && (a196202(n) < a196202(precprime(n-1))) && (a196202(n) < a196202(nextprime(n+1)))

Crossrefs

Cf. A000040, A001220, A196202.

Sequence in context: A059647 A059310 A299929 * A101324 A216830 A348933

Adjacent sequences: A287214 A287215 A287216 * A287218 A287219 A287220

Keyword

nonn

Author

Felix Fröhlich, May 27 2017

Status

approved