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A176416
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Fixed point of morphism 0->0PPMM00, P->0PPMM0P, M=0PPMM0M (where P=+1, M=-1)
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3
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0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, -1, 0, 1, 1, -1, -1, 0, -1, 0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, -1, 0, 1
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OFFSET
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0,1
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COMMENTS
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Turns by 120 degrees of a dragon curve (see fxtbook link below).
Also fixed point of morphism F->F0FPFPFMFMF0F, 0->0, P->P, M->M (after deleting all F).
Let d(n) be the lowest nonzero digit in the radix-7 expansion of (n+1), then if d(n)==[1,2,3,4,5,6] ==> a(n):=[0,+1,+1,-1,-1,0].
This is a 7-automatic sequence. - Joerg Arndt, Nov 09 2023
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LINKS
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MATHEMATICA
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Nest[Flatten[ReplaceAll[#, {-1->{0, 1, 1, -1, -1, 0, -1}, 0->{0, 1, 1, -1, -1, 0, 0}, 1->{0, 1, 1, -1, -1, 0, 1}}]]&, {0}, 3] (* Paolo Xausa, Nov 09 2023 *)
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PROG
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(C++) /* CAT-algorithm */
int bit_dragon_r7_2_turn(unsigned long &x)
/* Increment the radix-7 word x and return (tr)
according to the lowest nonzero digit d of the incremented word:
d==[1, 2, 3, 4, 5, 6] ==> rt:=[0, +1, +1, -1, -1, 0] */
{
unsigned long s = 0;
while ( (x & 7) == 6 ) { x >>= 3; ++s; } /* scan over nines */
++x; /* increment next digit */
int tr = 2 - ( (0x2f58 >> (2*(x&7)) ) & 3 ); x <<= (3*s); /* shift back */
return tr;
}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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