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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 Michel Dekking and Mike Keane, Two-block substitutions and morphic words, arXiv:2202.13548 [math.CO], 2022. 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: A308644 A308184 A114280 * A036466 A065882 A276327 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 April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)