A075302 Transpose of array A075300.

0, 2, 1, 4, 5, 3, 6, 9, 11, 7, 8, 13, 19, 23, 15, 10, 17, 27, 39, 47, 31, 12, 21, 35, 55, 79, 95, 63, 14, 25, 43, 71, 111, 159, 191, 127, 16, 29, 51, 87, 143, 223, 319, 383, 255, 18, 33, 59, 103, 175, 287, 447, 639, 767, 511, 20, 37, 67, 119, 207, 351, 575, 895, 1279

Offset: 0

Author

Antti Karttunen, Sep 12 2002

Keywords

• nonn
• tabl

Comments

The top-left corner of the array looks like:

0 2 4 6 8 10 12 14 ...

1 5 9 13 17 21 25 29 ...

3 11 19 27 35 43 51 59 ...

7 23 39 55 71 87 ...

15 47 79 ...

This can be used to construct mappings like A059884 and A075173, where the elements of the first row give the bit-positions where to interleave the first element of a finite vector of nonnegative integers, the second row the bit-positions for the second element, etc.

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A075303. Transpose: A075300. The X-projection is given by A025480 and the Y-projection is A007814(n+1). Cf. A002262, A025581.

Programs

Maple

A075302 := n -> A075300bi(A002262(n), A025581(n));
A075300bi := (x,y) -> (2^x * (2*y + 1))-1;
A002262 := n -> n - binomial(floor((1/2)+sqrt(2*(1+n))),2);
A025581 := n -> binomial(1+floor((1/2)+sqrt(2*(1+n))),2) - (n+1);