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 A274170 Christoffel words as binary numbers. 2
 2, 4, 6, 8, 14, 16, 20, 26, 30, 32, 62, 64, 72, 84, 106, 118, 126, 128, 164, 218, 254, 256, 272, 340, 426, 494, 510, 512, 584, 950, 1022, 1024, 1056, 1160, 1316, 1364, 1706, 1754, 1910, 2014, 2046, 2048, 2708, 3434, 4094, 4096, 4160, 4368, 4680, 5284, 5460, 6826, 7002, 7606, 7918, 8126, 8190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Christoffel word of slope b/a is defined as follows: Start at (0,0) in the 2-dimensional integer lattice and move up if possible, otherwise right, always keeping below or on the line y = b*x/a. Write down x for a horizontal move and y for a vertical move. The first move is necessarily horizontal, so the sequence always begins with x. Stop when you get to (a,b). The word then has length a+b and contains a copies of x and b of y (see Berstel et al., p. 6, Fig. 2). The symbols x and y are arbitrary: we replace x with 1 and y with 0 and treat the resulting word as a binary number. The sequence is in increasing order of decimal equivalents. The Christoffel word with least decimal equivalent is 10 with decimal equivalent 2. REFERENCES J. Berstel et al., Combinatorics on Words: Christoffel Words and Repetitions in Words, Amer. Math. Soc., 2008. LINKS EXAMPLE The Christoffel word of slope 4/7 is xxyxxyxxyxy which becomes 11011011010 with decimal equivalent 1754. MAPLE christoffel := proc (a, b) local n, x, y, ans; x := 1; y := 0; ans := 2^(a+b-1); for n to a+b-1 do if y+1 <= a*x/b then y := y+1 else ans := ans+2^(a+b-n-1); x := x+1 end if end do; ans end proc; for n from 2 to 12 do for b to n-1 do a := n-b; if gcd(a, n) = 1 then printf("%4d, ", christoffel(a, b)) end if end do end do CROSSREFS Cf. A144595-A144602 (with slightly different definition of Christoffel word). Sequence in context: A344001 A152973 A089747 * A173144 A049015 A005250 Adjacent sequences:  A274167 A274168 A274169 * A274171 A274172 A274173 KEYWORD easy,nonn AUTHOR Jamie Simpson, Jun 11 2016 STATUS approved

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Last modified May 18 03:30 EDT 2022. Contains 353783 sequences. (Running on oeis4.)