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 A175337 Fixed point of morphism 0 -> 00110, 1 -> 00111 4
 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Turns (by 90 degrees) of a dragon curve (called R5-dragon in the fxtbook, see link below) which can be rendered as follows: [Init] Set n=0 and direction=0. [Draw] Draw a unit line (in the current direction). Turn left/right if a(n) is zero/nonzero respectively. [Next] Set n=n+1 and goto (draw). With counting in radix 5: whether the lowest nonzero digit is >2 (see C++ code). With morphism F -> F0F0F1F1F, 0 -> 0, 1 -> 1: fixed point with all 'F' omitted. LINKS Paolo Xausa, Table of n, a(n) for n = 0..10000 Joerg Arndt, Matters Computational (The Fxtbook), section 1.31.5 "Dragon curves based on radix-R counting", pp.95-101; image on p.96 MATHEMATICA Nest[Flatten[ReplaceAll[#, {0->{0, 0, 1, 1, 0}, 1->{0, 0, 1, 1, 1}}]]&, {0}, 3] (* Paolo Xausa, Nov 09 2023 *) PROG (C++) /* CAT algorithm */ bool bit_dragon_r5_turn(ulong &x) /* Increment the radix-5 word x and return (tr) whether the lowest nonzero digit of the incremented word is > 2. */ { ulong s = 0; while ( (x & 7) == 4 ) { x >>= 3; ++s; } /* scan over nines */ bool tr = ( (x & 7) >= 2 ); /* whether digit will be > 2 */ ++x; /* increment next digit */ x <<= (3*s); /* shift back */ return tr; } CROSSREFS Cf. A080846 (with terdragon curve) and A014577 (with Heighway dragon). Sequence in context: A287382 A074290 A091225 * A285031 A327222 A286063 Adjacent sequences: A175334 A175335 A175336 * A175338 A175339 A175340 KEYWORD nonn AUTHOR Joerg Arndt, Apr 15 2010 STATUS approved

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Last modified December 8 13:40 EST 2023. Contains 367679 sequences. (Running on oeis4.)