A216164 Period of powers of 7 mod 10^n.

4, 4, 20, 100, 500, 5000, 50000, 500000, 5000000, 50000000, 500000000, 5000000000, 50000000000, 500000000000, 5000000000000, 50000000000000, 500000000000000, 5000000000000000, 50000000000000000, 500000000000000000

Offset: 1

Author

V. Raman, Sep 02 2012

Keywords

• nonn
• base
• easy

Comments

Essentially the same as A216099.

Links

• Index entries for linear recurrences with constant coefficients, signature (10).

Crossrefs

Cf. A000420, A216156, A216099

Programs

Mathematica

Join[{4, 4, 20, 100}, NestList[10*# &, 500, 20]] (* Paolo Xausa, Feb 19 2024 *)

Formula

a(n) = 4*5^(n-2), 1 < n < 5.

a(n) = 5*10^(n-3), n >= 5.

a(n) = 2^(n-3)*5^(n-2) for n>4. a(n) = 10*a(n-1) for n>5. G.f.: 4*x*(125*x^4 +25*x^3 +5*x^2 +9*x -1) / (10*x -1). - Colin Barker, Sep 22 2013