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

0,2

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

Table of n, a(n) for n=0..63.

Index entries for sequences that are permutations of the natural numbers

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);

Crossrefs

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

Sequence in context: A354699 A239806 A330402 * A352520 A350313 A257911

Adjacent sequences: A075299 A075300 A075301 * A075303 A075304 A075305

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 12 2002

Status

approved