A001903 Final digit of 7^n.

1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1

Offset

0,2

Comments

Period 4: repeat [1, 7, 9, 3]. - Joerg Arndt, Aug 12 2014

Links

Derek Orr, Table of n, a(n) for n = 0..1000

Edward Omey and Stefan Van Gulck, What are the last digits of ...?, International Journal of Mathematical Education in Science and Technology, (2015) 46:1, 147-155.

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) = 7^n mod 10. - Zerinvary Lajos, Nov 03 2009

From R. J. Mathar, Apr 20 2010: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) for n > 2.

G.f.: ( 1+6*x+3*x^2 ) / ( (1-x)*(1+x^2) ). (End)

a(n) = 10 - a(n-2) for n > 1. - Vincenzo Librandi, Feb 08 2011

From Bruno Berselli, Feb 08 2011: (Start)

a(n) = 5 - (2-i)*(-i)^n - (2+i)*i^n, where i=sqrt(-1).

a(n) = A001148(A159966(n)). (End)

a(n) = A010879(A000420(n)). - Michel Marcus, Jul 06 2016

E.g.f.: 2*sin(x) - 4*cos(x) + 5*exp(x). - Ilya Gutkovskiy, Jul 06 2016

Maple

A001903:=n->7^n mod 10: seq(A001903(n), n=0..100); # Wesley Ivan Hurt, Aug 12 2014

Mathematica

Table[PowerMod[7, n, 10], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)

Prog

(Sage) [power_mod(7, n, 10)for n in range(0, 81)] # Zerinvary Lajos, Nov 03 2009
(Magma)[7^n mod 10: n in [0..57]]; // Vincenzo Librandi, Feb 08 2011
(PARI) a(n)=lift(Mod(7, 10)^n) \\ Charles R Greathouse IV, Dec 28 2012

Crossrefs

Cf. A000420, A001148, A010879, A131707, A159966.

Sequence in context: A110793 A199290 A309644 * A011345 A201770 A377935

Adjacent sequences: A001900 A001901 A001902 * A001904 A001905 A001906

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved