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URL: https://oeis.org/A001903

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A001903
Final digit of 7^n.
5
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
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.
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 *)
LinearRecurrence[{1, -1, 1}, {1, 7, 9}, 100] (* or *) PadRight[{}, 100, {1, 7, 9, 3}] (* Harvey P. Dale, May 21 2025 *)
PROG
(SageMath) [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
KEYWORD
nonn,easy
STATUS
approved