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A175337 Fixed point of morphism 0 -> 00110, 1 -> 00111 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, 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

Table of n, a(n) for n=0..104.

Joerg Arndt, Fxtbook, section 1.31.5 "Dragon curves based on radix-R counting", pp.95-101; image on p.96

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: A043545 A094754 A091225 * A132380 A021913 A156660

Adjacent sequences:  A175334 A175335 A175336 * A175338 A175339 A175340

KEYWORD

nonn

AUTHOR

Joerg Arndt, Apr 15 2010

STATUS

approved

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Last modified April 19 08:09 EDT 2014. Contains 240739 sequences.