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

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• cons
• easy

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

Decimal expansion of 16/99. - Stefano Spezia, Feb 09 2025

Examples

			0.1616161616161616161616161616161616161616161616161...
		

Links

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

Programs

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 *)

PARI

a(n)=n%2*5+1 \\ Charles R Greathouse IV, Jul 13 2016

Sage

[power_mod(6,n,7)for n in range(0,100)] # Zerinvary Lajos, Nov 26 2009

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

E.g.f.: cosh(x) + 6*sinh(x). - Stefano Spezia, Feb 09 2025