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.

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

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 A334840

Adjacent sequences: A065656 A065657 A065658 * A065660 A065661 A065662

Keyword

nonn,tabl

Author

Antti Karttunen, Nov 22 2001

Status

approved