A069705 a(n) = 2^n mod 7.

1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4

Offset: 0

Author

Jon Perry, Jan 14 2003

Keywords

• nonn
• easy

Comments

Periodic sequence with period [1,2,4]. - Philippe Deléham, Sep 25 2006

From Klaus Brockhaus, May 23 2010: (Start)

Continued fraction expansion of (11 + sqrt(229))/18.

Decimal expansion of 124/999. (End)

Examples

			a(4)=16 mod 7=2, a(5)=32 mod 7=4, a(6)=64 mod 7=1.
		

Links

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

Crossrefs

Cf. A000079, A050985.

Cf. A178233 (decimal expansion of (11+sqrt(229))/18).

Cf. A052901, A144437.

Programs

GAP

List([0..83],n->PowerMod(2,n,7)); # Muniru A Asiru, Jan 31 2019

Magma

[Modexp(2, n, 7): n in [0..100]]; // Vincenzo Librandi, Mar 25 2016

Maple

A069705 := proc(n) op((n mod 3)+1,[1,2,4]) ; end proc: # R. J. Mathar, Feb 05 2011

Mathematica

PowerMod[2,Range[0,110],7] (* or *) PadRight[{},110,{1,2,4}] (* Harvey P. Dale, Mar 28 2015 *)

PARI

a(n)=2^(n%3)%7 \\ Charles R Greathouse IV, Jun 11 2015

PARI

a(n) = lift(Mod(2, 7)^n); \\ Altug Alkan, Mar 25 2016

Sage

[power_mod(2,n,7) for n in range(0, 105)] # Zerinvary Lajos, Jun 07 2009

Formula

n=0 mod 3 -> a(n)=1 n=1 mod 3 -> a(n)=2 n=2 mod 3 -> a(n)=4.

a(n) = 2^(n mod 3). - Paul Barry, Oct 06 2003

a(n) = cubefree part of 2^n = A000079(A050985(n)). - Artur Jasinski, Oct 15 2008

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-3).

G.f.: (1+2*x+4*x^2)/((1-x) * (1+x+x^2)). (End)

a(n) = (7+5*cos(2*(n+1)*Pi/3)-sqrt(3)*sin(2*(n+1)*Pi/3))/3. - Wesley Ivan Hurt, Oct 01 2017

From Nicolas Bělohoubek, Nov 11 2021: (Start)

a(n) = 8/(a(n-2)*a(n-1)).

a(n) = 7 - a(n-2) - a(n-1). See also A052901 or A144437. (End)

a(n) = n + 1 + floor((n+1)/3) - 4*floor(n/3). - Ridouane Oudra, Sep 25 2024

E.g.f.: (7*exp(x) - 2*exp(-x/2)*(2*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/3. - Stefano Spezia, Sep 27 2024