A065630 -id:A065630 - cp's OEIS frontend

A065629 Permutation of N induced by rotating the node 3 right in the infinite planar binary tree. The third row of A065625. Inverse of A065630.

1, 2, 7, 4, 5, 3, 15, 8, 9, 10, 11, 6, 14, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 28, 29, 60, 61, 62, 63, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 56, 57, 58, 59, 120, 121, 122, 123, 124, 125, 126, 127, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91

Offset: 1

Antti Karttunen, Nov 08 2001

nonn

Index entries for sequences that are permutations of the natural numbers

Stabilizes the set A004761.

Maple
```
[seq(RotateNodeRight(3,j),j=1..120)];
```

A065626 Table of permutations of N, each row being a generator of the "rotation group" of infinite planar binary tree. Inverse generators are given in A065625.

Original entry on oeis.org

2, 4, 1, 1, 4, 1, 8, 3, 2, 1, 9, 8, 6, 2, 1, 5, 2, 4, 3, 2, 1, 3, 6, 5, 8, 3, 2, 1, 16, 7, 12, 5, 4, 3, 2, 1, 17, 16, 3, 6, 10, 4, 3, 2, 1, 18, 17, 8, 7, 6, 5, 4, 3, 2, 1, 19, 9, 9, 16, 7, 12, 5, 4, 3, 2, 1, 10, 5, 10, 4, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 11, 10, 9, 8, 14, 6, 5, 4, 3, 2, 1, 6, 13, 24, 11, 20, 9, 8, 7, 6, 5, 4, 3, 2, 1, 7, 14, 25, 12, 5, 10, 9, 16, 7, 6, 5, 4, 3, 2

Offset: 0

Antti Karttunen, Nov 08 2001

The first row (rotate the top node left): A057115, 2nd row (rotate the top node's left child): A065628, 3rd row (rotate the top node's right child): A065630, 4th row: A065632, 5th row: A065634, 6th row: A065636, 7th row: A065638, 8th row: A065640. Maple procedure floor_log_2 given in A054429, for trinv, follow A065167.

[seq(RotateLeftTable(j),j=0..119)];
RotateLeftTable := n -> RotateNodeLeft(1+(n-((trinv(n)*(trinv(n)-1))/2)),(((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1);
# Rewrites t-prefixed x's in the following way: t -> t0, t0... -> t00..., t1 -> t, t10... -> t01..., t11... -> t1... and leaves other x's intact.
RotateNodeLeft := proc(t,x) local u,y; u := floor_log_2(t)+1; y := floor_log_2(x)+1; if(y < u) then RETURN(x); fi; if(floor(x/(2^(y-u))) <> t) then RETURN(x); fi; if(x = t) then RETURN(2*x); fi; if(0 = (floor(x/(2^(y-u-1))) mod 2)) then RETURN(x + (t * 2^(y-u))); fi; if(y = (u+1)) then RETURN((x-1)/2); fi; if(0 = (floor(x/(2^(y-u-2))) mod 2)) then RETURN(x - 2^(y-u-2)); fi; RETURN(x - ((t+1) * 2^(y-u-1))); end;

cp's OEIS Frontend

A065629 Permutation of N induced by rotating the node 3 right in the infinite planar binary tree. The third row of A065625. Inverse of A065630.

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