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Search: id:A008959
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| A008959 |
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Final digits of squares. |
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+0
8
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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; listen)
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OFFSET
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0,3
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COMMENT
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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]
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LINKS
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Index entries for sequences related to final digits of numbers
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FORMULA
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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 (ppl(AT)spl.at), 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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PROGRAM
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(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
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a(n) = A010879(A000290(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 04 2009]
A070431, A070435, A070438, A070442, A070452, A159852, A000290. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2009]
Sequence in context: A163103 A019688 A094090 this_sequence A059729 A108533 A075635
Adjacent sequences: A008956 A008957 A008958 this_sequence A008960 A008961 A008962
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KEYWORD
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nonn,easy,base,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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