A196627 Primes p such that the system of congruences { 2^x == 3 (mod p), 3^x == 2 (mod p) } has a solution.

5, 5333, 18414001, 804146449, 1117131202441, 11170373961701, 92009554676141, 110451862680769

Offset

1,1

Comments

Prime divisors of the elements of A109768.

The corresponding smallest positive solutions x are given by A196628.

Some larger terms: 600827908214213, 18969653181299397175271, 1098445767808750903973251, 364947672292511454405089069, 706132008101135602203621405289, 203315521506434771079581843014801, 29579867253585988507046633033646287, 183139575629088302014027581573180839, 59813046375181769306016700165290169537, 1517811599380242183731391003255018381040066573726286733611752067380771.

This sequence has density zero among all primes. More exactly, M. Skałba showed that the number of terms in this sequence below x is O(x/(log(x))^1.0243). -Tomohiro Yamada, Jul 17 2019

Links

Table of n, a(n) for n=1..8.

A. S. Izotov, On prime divisors of GCD(3^n-2,2^n-3), Fibonacci Quarterly 43, May 2005, pp. 130-131.

M. Skałba, Primes dividing both 2^n-3 and 3^n-2 are rare, Archiv der Mathematik 84 (2005), issue 6, pp. 485-495.

Crossrefs

Sequence in context: A086896 A177503 A072021 * A013535 A079812 A137694

Adjacent sequences: A196624 A196625 A196626 * A196628 A196629 A196630

Keyword

nonn,hard,more

Author

Max Alekseyev, Oct 04 2011

Status

approved