A305192 Primes p such that the residues 2^(p-1) (mod p^3) and 2^(p-1) (mod p^2) are equal.

2, 3, 5, 33050029

Offset

1,1

Comments

Primes p such that A271234(i) = A196202(i), where i is the index of p in A000040.

2, 3 and 5 are "trivially" terms of the sequence, since for those primes 2^(p-1) < p^2.

Are any Wieferich primes (A001220) in this sequence?

a(5) > 7*10^12, if it exists. - Giovanni Resta, Jun 12 2018

Links

Table of n, a(n) for n=1..4.

Example

The residues 2^(p-1) (mod p^3) and 2^(p-1) (mod p^2) for a(1)-a(4) are both 2, 4, 16 and 958996926629168, respectively.

Prog

(PARI) is(n) = lift(Mod(2, n^3)^(n-1))==lift(Mod(2, n^2)^(n-1))
forprime(p=1, , if(is(p), print1(p, ", ")))

Crossrefs

Cf. A000040, A001220, A196202, A271234.

Sequence in context: A335304 A193888 A361312 * A141186 A078682 A331205

Adjacent sequences: A305189 A305190 A305191 * A305193 A305194 A305195

Keyword

nonn,hard,more

Author

Felix Fröhlich, May 27 2018

Status

approved