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A065659 The table of permutations of N, each row induced by the rotation (to the left) of the n-th node in the infinite binary "decimal" fraction tree. 8
4, 16, 1, 22, 136, 1, 64, 3, 2, 1, 8, 64, 25, 2, 1, 160, 19, 4, 3, 76, 1, 1, 6, 5, 4, 3, 2, 1, 256, 7, 97, 5, 4, 3328, 2, 1, 32, 256, 13, 6, 167772160, 4, 3, 2, 1, 67, 1054, 8, 7, 6, 5, 4, 3, 2, 1, 34, 4, 9, 130, 7, 97, 5, 4, 3, 1249, 1, 1279, 40, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See the comment at A065658.

LINKS

Table of n, a(n) for n=0..79.

Index entries for sequences related to Stern's sequences

MAPLE

[seq(RotateBinFracLeftTable(j), j=0..119)]; RotateBinFracLeftTable := n -> RotateBinFracNodeLeft(1+(n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1);

RotateBinFracNodeLeft := (t, n) -> frac2position_in_0_1_SB_tree(RotateBinFracNodeLeft_x(t, SternBrocot0_1frac(n)));

RotateBinFracNodeLeft_x := proc(t, x) local num, den; den := 2^(1+floor_log_2(t)); num := (2*(t-(den/2)))+1; if((x <= (num-1)/den) or (x >= (num+1)/den)) then RETURN(x); fi; if(x >= ((2*num)+1)/(2*den)) then RETURN(((num-1)/den) + (2*(x - (num/den)))); fi; if(x > (num/den)) then RETURN(x - (1/(2*den))); fi; RETURN(((num-1)/den) + ((x-((num-1)/den))/2)); end;

SternBrocot0_1frac := proc(n) local m; m := n + 2^floor_log_2(n); SternBrocotTreeNum(m)/SternBrocotTreeDen(m); end;

frac2position_in_0_1_SB_tree := r -> RETURN(ReflectBinTreePermutation(cfrac2binexp(convert(1/r, confrac))));

CROSSREFS

The first row (rotate the top node left): A065661, 2nd row (rotate the top node's left child): A065663, 3rd row (rotate the top node's right child): A065665, 4th row: A065667, 5th row: A065669, 6th row: A065671, 7th row: A065673. Cf. also A065674-A065676. For the other needed Maple procedures follow A065658 which gives the inverse permutations.

Sequence in context: A228559 A165410 A016486 * A305833 A110650 A232515

Adjacent sequences:  A065656 A065657 A065658 * A065660 A065661 A065662

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Nov 22 2001

STATUS

approved

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Last modified January 19 16:32 EST 2019. Contains 319309 sequences. (Running on oeis4.)