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A133145 Period 4: repeat [1, 2, 4, 8]. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Terms of the simple continued fraction of 13/(sqrt(3363)-49). Decimal expansion of 416/3333. [Paolo P. Lava, Aug 05 2009]

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) = (1/8)*{19*(n mod 4)-3*[(n+1) mod 4]+[(n+2) mod 4]+3*[(n+3) mod 4]}. - Paolo P. Lava, Jul 03 2008

a(n) = 15/4-(3/4-(3/2)*I)*I^n-(5/4)*(-1)^n-(3/4+(3/2)*I)*(-I)^n. - Paolo P. Lava, Jul 17 2008

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

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

a(n) = 2^n (mod 15). G.f.: (1+2*x)*(4*x^2+1)/ ((1-x)*(1+x)*(x^2+1)). [R. J. Mathar, Apr 13 2010]

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)

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

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

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

CROSSREFS

Cf. A069705. [Jaume Oliver Lafont, Mar 27 2009]

Cf. A000079, A160700.

Sequence in context: A010743 A072032 A023104 * A317414 A008952 A268516

Adjacent sequences:  A133142 A133143 A133144 * A133146 A133147 A133148

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 16 2007

STATUS

approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)