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 A070366 a(n) = 5^n mod 9. 14
 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Period 6: repeat [1, 5, 7, 8, 4, 2]. Also the digital root of 5^n. - Cino Hilliard, Dec 31 2004 Digital root of the powers of any number congruent to 5 mod 9. - Alonso del Arte, Jan 26 2014 REFERENCES Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1). FORMULA a(n) = (1/30) * {14 * (n mod 6) + 19 * [(n+1) mod 6] + 29*[(n+2) mod 6] + 4 * [(n+3) mod 6] - [(n+4) mod 6] - 11 * [(n+5) mod 6]}. - Paolo P. Lava, Feb 24 2010 From R. J. Mathar, Apr 20 2010: (Start) a(n) = a(n-1) - a(n-3) + a(n-4) for n>3. G.f.: ( 1+4*x+2*x^2+2*x^3 ) / ( (1-x)*(1+x)*(x^2-x+1) ). (End) a(n) = 1/2^n (mod 9), n >= 0. - Wolfdieter Lang, Feb 18 2014 a(n) = A010878(A000351(n)). - Michel Marcus, Feb 20 2014 From G. C. Greubel, Mar 05 2016: (Start) a(n) = a(n-6) for n>5. E.g.f.: (1/2)*(9*exp(x) - exp(-x) + 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) - 6*exp(x/2)*cos(sqrt(3)*x/2)). (End) a(n) = (9 - cos(n*Pi) - 6*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/2. - Wesley Ivan Hurt, Jun 28 2016 a(n) = 2^((-n) mod 6) mod 9. - Joe Slater, Mar 23 2017 MAPLE A070366:=n->power(5, n) mod 9: seq(A070366(n), n=0..100); # Wesley Ivan Hurt, Jun 28 2016 MATHEMATICA PowerMod[5, Range[0, 120], 9] (* Harvey P. Dale, Mar 27 2011 *) Table[Mod[5^n, 9], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *) PROG (PARI) a(n)=lift(Mod(5, 9)^n); \\ Charles R Greathouse IV, Sep 24 2015 (MAGMA) [Modexp(5, n, 9): n in [0..100]]; // Wesley Ivan Hurt, Jun 28 2016 CROSSREFS Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 4, A100402; c = 7, A070403; c = 8, A010689. Cf. A000351, A010878. Sequence in context: A244355 A245278 A155855 * A141606 A197491 A254274 Adjacent sequences:  A070363 A070364 A070365 * A070367 A070368 A070369 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 12 2002 STATUS approved

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Last modified November 18 14:06 EST 2017. Contains 294892 sequences.