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 A008960 Final digit of cubes: n^3 mod 10. 16
 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Decimal expansion of 208284810/1111111111. - Alexander R. Povolotsky, Mar 08 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1). FORMULA Periodic with period 10. - Franklin T. Adams-Watters, Mar 13 2006 a(n) = 1/5*(5*(n mod 10)-3*((n+1) mod 10)+((n+2) mod 10)+2*((n+3) mod 10)+2*((n+6) mod 10)+((n+7) mod 10)-3*((n+8) mod 10)). - Paolo P. Lava, Nov 24 2006 a(n) = 4.5 -cos(Pi*n/5) +(1/2*(-(5-5^(1/2))^(1/2) +(5+5^(1/2))^(1/2))*2^(1/2))*sin(Pi*n/5) -cos(2*Pi*n/5) +(-1/10*(-(5-5^(1/2))^(1/2)+3*(5+5^(1/2))^(1/2))*2^(1/2))*sin(2*Pi*n/5) -cos(3*Pi*n/5) +(-1/2*((5-5^(1/2))^(1/2) +(5+5^(1/2))^(1/2))*2^(1/2))*sin(3*Pi*n/5) -cos(4*Pi*n/5) +( -1/10*(3*(5-5^(1/2))^(1/2) +(5 +5^(1/2))^(1/2))*2^(1/2))*sin(4*Pi*n/5) -0.5*(-1)^n. - Richard Choulet, Dec 12 2008 a(n) = n^k mod 10; for k > 0 where k mod 4 = 3. - Doug Bell, Jun 15 2015 G.f.: x*(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)). - Colin Barker, Nov 30 2015 MATHEMATICA Table[Mod[n^3, 10], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 8, 7, 4, 5, 6, 3, 2, 9}, 81] (* Ray Chandler, Aug 26 2015 *) PROG (Sage) [power_mod(n, 3, 10 ) for n in range(0, 81)] # Zerinvary Lajos, Oct 29 2009 (PARI) a(n)=n^3%10 \\ Charles R Greathouse IV, Mar 08 2013 (MAGMA) [n^3 mod 10: n in [0..80]]; // Vincenzo Librandi, Mar 26 2013 (PARI) concat(0, Vec(x*(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)) + O(x^100))) \\ Colin Barker, Nov 30 2015 CROSSREFS Cf. A167176. Cf. A010879, A008959, A070514. - Doug Bell, Jun 15 2015 Sequence in context: A249136 A154815 A085848 * A077744 A111448 A169885 Adjacent sequences:  A008957 A008958 A008959 * A008961 A008962 A008963 KEYWORD nonn,easy,base AUTHOR STATUS approved

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Last modified April 11 05:30 EDT 2021. Contains 342886 sequences. (Running on oeis4.)