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A008959
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Final digits of squares: n^2 mod 10.
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11
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0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(m*n)=a(m)*a(n) mod 10; a(5*n+k)=a(5*n-k) for k<=5*n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2009]
n^6 mod 10. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]
a(n) = A002015(n) mod 10 = A174452(n) mod 10. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 21 2010]
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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*{(n mod 10)+2*[(n+1) mod 10]+3*[(n+2) mod 10]-[(n+3) mod 10]+[(n+5) mod 10]+2*[(n+6) mod 10]-2*[(n+7) mod 10]-[(n+8) mod 10]} - Paolo P. Lava (paoloplava(AT)gmail.com), Nov 24 2006
a(n)=4.5 - (1 + 5^(1/2))*cos(Pi*n/5) + ( - 1 - 3/5*5^(1/2))*cos(2*Pi*n/5) + (5^(1/2) - 1)*cos(3*Pi*n/5) + ( - 1 + 3/5*5^(1/2))*cos(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^2, 10], {n, 0, 200}] (* From Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
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PROG
| (Other) sage: [power_mod(n, 6, 10)for n in xrange(0, 81)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]
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CROSSREFS
| a(n) = A010879(A000290(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 04 2009]
Cf. A070431, A070435, A070438, A070442, A070452, A159852, A000290. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2009]
Sequence in context: A094090 A200632 A186723 * A169917 A059729 A184988
Adjacent sequences: A008956 A008957 A008958 * A008960 A008961 A008962
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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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