[seqfan] The primality test

[юрий герасимов]

Dear SequFans, what Carmichael number r (> 10^8) is the least pseudoprime for the next primality test:
a(n) is numbers r such that the number of nonnegative m < (r+1) such that m^(r+1) == m (mod (r+1)) is equal to (the number of nonnegative m < (r+1) such that -m^(r+1) == m (mod (r+1)))*r and the number of nonnegative m < (r+1) such that m^k == m (mod (r+1)) is equal to (the number of nonnegative m < (r+1) such that -m^k == m (mod (r+1)))*k, where k = 2^ https://oeis.org/A007814 A007814 (r) + 1?
P. S. The weakness of MAGMA-calculator allowed me to limit muself only an interval of up to 10^8.