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A133145

Period 4: repeat [1, 2, 4, 8].

1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..79.

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

FORMULA

a(n) == 2*a(n-1) mod 15.

a(n) = 2^(n mod 4). - Jaume Oliver Lafont, Mar 27 2009

a(n) = A160700(A000079(n)). - Reinhard Zumkeller, Jun 10 2009

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

a(n) = 2^n (mod 15).

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

From Wesley Ivan Hurt, Jul 09 2016: (Start)

a(n) = a(n-4) for n>3.

a(n) = (15-6*cos(n*Pi/2)-5*cos(n*Pi)-12*sin(n*Pi/2)-5*I*sin(n*Pi))/4. (End)

E.g.f.: 5*cosh(x)/2 - 3*(cos(x) + 2*sin(x))/2 + 5*sinh(x). - Stefano Spezia, Oct 30 2025

MAPLE

seq(op([1, 2, 4, 8]), n=0..50); # Wesley Ivan Hurt, Jul 09 2016

MATHEMATICA

PadRight[{}, 100, {1, 2, 4, 8}] (* Wesley Ivan Hurt, Jul 09 2016 *)

Table[First@ IntegerDigits[2^n, 16], {n, 0, 120}] (* Michael De Vlieger, Jul 09 2016 *)

PROG

(PARI) a(n)=2^(n%4) \\ Jaume Oliver Lafont, Mar 27 2009

(SageMath) [power_mod(2, n, 15) for n in range(0, 80)] # Zerinvary Lajos, Nov 03 2009

(Magma) &cat [[1, 2, 4, 8]^^30]; // Wesley Ivan Hurt, Jul 09 2016

CROSSREFS

Cf. A069705.

Cf. A000079, A160700.

Sequence in context: A072032 A365814 A023104 * A350208 A317414 A008952

Adjacent sequences: A133142 A133143 A133144 * A133146 A133147 A133148

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 16 2007

STATUS

approved

URL: https://oeis.org/A133145

⇱ A133145 - OEIS