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A305192
Primes p such that the residues 2^(p-1) (mod p^3) and 2^(p-1) (mod p^2) are equal.
0
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
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
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, May 27 2018
STATUS
approved