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A001903 Final digit of 7^n. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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]

a(n) = (1/3)*{4*(n mod 4)+7*[(n+1) mod 4]+[(n+2) mod 4]-2*[(n+3) mod 4]}. [Paolo P. Lava, Apr 16 2010]

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) ). [R. J. Mathar, Apr 20 2010]

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

a(n) = 5-(2-I)*(-I)^n-(2+I)*I^n. Also a(n) = A001148(A159966(n)). - Bruno Berselli, Feb 08 2011

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 xrange(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: A249546 A110793 A199290 * A011345 A201770 A086282

Adjacent sequences:  A001900 A001901 A001902 * A001904 A001905 A001906

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 27 22:02 EDT 2017. Contains 284182 sequences.