A014391 Final digit of 8^n.

1, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6, 8, 4, 2, 6

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for sequences related to final digits of numbers

Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Formula

a(n) = 8^n mod 10. [Zerinvary Lajos, Nov 27 2009]

G.f.: -(7*x - 3*x^2 + 5*x^3 + 1)/ ((x - 1)*(1 + x^2)). [R. J. Mathar, Apr 20 2010]

a(n) = +a(n-1) -a(n-2) +a(n-3). [R. J. Mathar, Apr 20 2010]

Mathematica

Table[PowerMod[8, n, 10], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
LinearRecurrence[{1, -1, 1}, {1, 8, 4, 2}, 100] (* Harvey P. Dale, Jul 01 2019 *)

Prog

(Sage) [power_mod(8, n, 10)for n in range(0, 105)] # Zerinvary Lajos, Nov 27 2009
(PARI) a(n)=lift(Mod(8, 10)^n) \\ Charles R Greathouse IV, Dec 29 2012
(Magma) [Modexp(8, n, 10): n in [0..100]]; // Vincenzo Librandi, Jun 30 2016

Crossrefs

Sequence in context: A010523 A231534 A348908 * A099286 A089729 A173670

Adjacent sequences: A014388 A014389 A014390 * A014392 A014393 A014394

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved