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A001903
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Final digit of 7^n.
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4
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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
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refs;
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OFFSET
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0,2
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COMMENTS
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Period 4: repeat [1, 7, 9, 3]. - Joerg Arndt, Aug 12 2014
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LINKS
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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).
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FORMULA
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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
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
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MAPLE
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A001903:=n->7^n mod 10: seq(A001903(n), n=0..100); # Wesley Ivan Hurt, Aug 12 2014
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MATHEMATICA
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Table[PowerMod[7, n, 10], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
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PROG
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(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
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CROSSREFS
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Cf. A000420, A001148, A010879, A131707, A159966.
Sequence in context: A110793 A199290 A309644 * A011345 A201770 A086282
Adjacent sequences: A001900 A001901 A001902 * A001904 A001905 A001906
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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