A010687 Repeat (1,6): Period 2.

1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6

Offset

0,2

Comments

Continued fraction for (3+sqrt(15))/6. - Philippe Deléham, Sep 25 2006

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 can be congruent to either 3,5 or 6 mod 7. If a is congruent to 3 or 5 mod 7 then b can be any number of the form 3*k+6. If a is congruent to 6 mod 7 then b can be any number of the form 2k+1. Finally, if a is congruent to either 6, 26, or 31 mod 35 then c can be 7 or 35; otherwise, we use c = 7. For example: a(n) = 33^(15*n) mod 7, a(n) = 31^(9*n) mod 7, and a(n) = 31^(9*n) mod 35. - Gary Detlefs, May 19 2014

Links

Table of n, a(n) for n=0..85.

Index entries for linear recurrences with constant coefficients, signature (0,1).

Formula

G.f.: (1+6*x)/(1-x^2). - Philippe Deléham, Sep 25 2006

a(n) = 6^n mod 7. - Zerinvary Lajos, Nov 26 2009

Maple

A010687:=n->(6^n mod 7); seq(A010687(n), n=0..100); # Wesley Ivan Hurt, May 19 2014

Mathematica

Table[Mod[6^n, 7], {n, 0, 100}] (* Wesley Ivan Hurt, May 19 2014 *)

Prog

(Sage) [power_mod(6, n, 7)for n in range(0, 100)] # Zerinvary Lajos, Nov 26 2009
(PARI) a(n)=n%2*5+1 \\ Charles R Greathouse IV, Jul 13 2016

Crossrefs

Sequence in context: A348999 A349000 A344699 * A176355 A109918 A339433

Adjacent sequences: A010684 A010685 A010686 * A010688 A010689 A010690

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1996

Status

approved