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A123564 The infinite Fibonacci word reencoded by writing successive non-overlapping pairs of bits as decimal numbers. 3
2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The algorithm used here suggests multiple variations such as using more than 2 bits, allowing overlap of successive subwords, using other numbers for the encoding of subwords or using other binary sequences. (E.g. overlapping: a(n) = 2*A005614(n) + A005614(n+1) )

Essentially equal to A143667. - Michel Dekking, Sep 26 2017

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

f = (sqrt(5)-1)/2; m = 2*n; a(n) = floor(m*f) - 2*floor((m-1)*f) + floor((m+1)*f);

a(n) = 2*A005614(2n-1) + A005614(2n), using the infinite Fibonacci word A005614.

EXAMPLE

a(1) = 2*1+0 = 2;

a(2) = 2*1+1 = 3;

a(3) = 2*0+1 = 1.

MATHEMATICA

f := 1/GoldenRatio; T[n_] := Floor[2*n*f] - 2*Floor[(2*n - 1)*f] + Floor[(2*n + 1)*f]; Transpose[{Range[1, 50], Table[T[n], {n, 1, 50}] (* G. C. Greubel, Oct 16 2017 *)

PROG

(PARI) f=(sqrt(5)-1)/2; a(n)= my(m=2*n); floor(m*f)-2*floor((m-1)*f)+floor((m+1)*f); \\ Michel Marcus, Sep 26 2017

CROSSREFS

Cf. A005614, A143667

Sequence in context: A266743 A284050 A114280 * A065882 A276327 A007884

Adjacent sequences:  A123561 A123562 A123563 * A123565 A123566 A123567

KEYWORD

easy,nonn

AUTHOR

Alexandre Losev, Nov 12 2006

STATUS

approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)