This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A010686 Periodic sequence: Repeat 1,5. 18
 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; text; internal format)
 OFFSET 0,2 COMMENTS 5^n mod 12. - Zerinvary Lajos, Nov 25 2009 Also continued fraction expansion of (5+3*sqrt(5))/10. - Bruno Berselli, Sep 30 2011 From Gary Detlefs, May 19 2014: (Start) This sequence can be generated by an infinite number of formulas all having the form a^(b*n) mod c subject to the following conditions. The number a is congruent to either 5,11,13,17,21, or 23 mod 24 and b is of the form 2k+1.   1. If a = 5 mod 6 then c = 6   2. If a = 5 mod 8 then c = 8   3. If a = 5 mod 12 then c = 12   4. If a = 5 mod 24 then c = 24 For example: a(n)= 13^(5*n) mod 8, a(n)= 29^(7*n) mod c where c is any number in {6,8,12,24}. (End) LINKS Burkard Polster, Juggling, maths and a beautiful mind [From Parthasarathy Nambi, Nov 20 2009] Index entries for linear recurrences with constant coefficients, signature (0,1). FORMULA 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 a(n) = 11^n mod 6. - Vincenzo Librandi, Jun 01 2016 MAPLE [seq (modp((4*n+1), 8), n=0..80)]; # Zerinvary Lajos, Dec 01 2006 MATHEMATICA PadRight[{}, 120, {1, 5}] (* Harvey P. Dale, Aug 19 2012 *) PROG (Sage) [power_mod(5, n, 12)for n in xrange(0, 101)] # - Zerinvary Lajos, Nov 25 2009 (Maxima) A010686(n):=if evenp(n) then 1 else 5\$ makelist(A010686(n), n, 0, 30); /* Martin Ettl, Nov 09 2012 */ (PARI) a(n)=n%2*4+1 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Sequence in context: A019840 A205109 A144432 * A021070 A176260 A098190 Adjacent sequences:  A010683 A010684 A010685 * A010687 A010688 A010689 KEYWORD nonn,easy AUTHOR EXTENSIONS Definition rewritten by Bruno Berselli, Sep 30 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)