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A010686
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Periodic sequence: Repeat 1,5.
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16
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1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 5^n mod 12. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2009]
Also continued fraction expansion of (5+3*sqrt(5))/10. - Bruno Berselli, Sep 30 2011
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LINKS
| Burkard Polster, Juggling, maths and a beautiful mind [From Parthasarathy Nambi, Nov 20 2009]
Index to sequences with linear recurrences with constant coefficients, signature (0,1).
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FORMULA
| Contribution from Paul Barry, Jun 03 2003: (Start)
G.f.: (1+5*x)/((1-x)*(1+x)).
E.g.f.: 3*exp(x)-2*exp(-x).
a(n) = 3-2(-1)^n.
a(n) = 5^((1-(-1)^n)/2) = 5^(ceiling(n/2)-floor(n/2)). (End)
a(n) = 5*(n mod 2)+(n+1) mod 2 - Paolo P. Lava, Oct 20 2006
a(n) = 5^n mod 24. - Paul Curtz, Jan 09 2008
a(n) = A000364(n+1) mod 10. - Paul Curtz, Feb 09 2010
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MAPLE
| [seq (modp((4*n+1), 8), n=0..80)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
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PROG
| (Other) sage: [power_mod(5, n, 12)for n in xrange(0, 101)] #o [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2009]
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CROSSREFS
| Sequence in context: A019840 A205109 A144432 * A021070 A176260 A098190
Adjacent sequences: A010683 A010684 A010685 * A010687 A010688 A010689
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Definition rewritten by Bruno Berselli, Sep 30 2011
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