A343410 a(n) is the smallest A (in absolute value) such that for p = prime(n), 3^{(p-1)/2} == +-1 + A*p (mod p^2), i.e., such that p is a base-3 near-Wieferich prime (near-Mirimanoff prime).

1, 2, 3, 0, 4, 5, 9, 3, 7, 7, 9, 10, 1, 18, 15, 9, 24, 26, 16, 13, 27, 32, 12, 45, 8, 10, 49, 4, 2, 30, 28, 9, 47, 6, 22, 47, 49, 50, 56, 43, 66, 55, 22, 14, 74, 9, 61, 96, 21, 25, 47, 22, 111, 64, 23, 5, 114, 128, 110, 121, 86, 56, 90, 156, 117, 48, 166, 133

Offset

2,2

Comments

a(n) = 0 if and only if p is a base-3 Wieferich prime (Mirimanoff prime, cf. A014127).

These values can be used in a search for Mirimanoff primes to define "near-Mirimanoff primes" by choosing some value x and reporting all primes with |A| <= x in order to get a larger dataset.

Links

Table of n, a(n) for n=2..69.

Prog

(PARI) a(n) = my(p=prime(n)); abs(centerlift(Mod(3, p^2)^((p-1)/2))\/p)

Crossrefs

Cf. A014127, A258367.

Sequence in context: A091246 A271439 A334655 * A133637 A258093 A286578

Adjacent sequences: A343407 A343408 A343409 * A343411 A343412 A343413

Keyword

nonn

Author

Felix Fröhlich, Apr 14 2021

Status

approved