[seqfan] Period of final n digits of 2^k

[Neil Sloane]

Dear Seq Fans,
Consider the sequence {2^k, k >= 0} mod 10^n. Let a(n) be its period.

2^k mod 10 is 1 2 4 8 6 2 4 8 6 ... which has period 4 (see A000689).  So
a(1) = 4.
a(2) = 20 (A000855).
a(3) = 100 (A126605) according to Zak Seidov, who also says that
a(4) = 500.

So 4, 20, 100, 500, ? : how does it continue? Is it A005054? But A005054
does not mention this property.  Someone please help!

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com