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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

Table of n, a(n) for n=0..80.

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

N. J. A. Sloane

EXTENSIONS

Definition rewritten by Bruno Berselli, Sep 30 2011

STATUS

approved

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Last modified October 22 04:29 EDT 2018. Contains 316431 sequences. (Running on oeis4.)