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A008960
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Final digits of cubes: n^3 mod 10.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to final digits of numbers
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FORMULA
| Periodic with period 10. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 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]} with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), 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 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 12 2008]
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MATHEMATICA
| Table[Mod[n^3, 10], {n, 0, 200}] (* From Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
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PROG
| (Sage) [power_mod(n, 3, 10 ) for n in xrange(0, 81)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 29 2009]
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CROSSREFS
| Cf. A167176.
Sequence in context: A072102 A154815 A085848 * A077744 A111448 A169885
Adjacent sequences: A008957 A008958 A008959 * A008961 A008962 A008963
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KEYWORD
| nonn,easy,base
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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