0,2

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.

Index entries for sequences that are permutations of the natural numbers

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);

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: A125751 A099492 A144203 this_sequence A028509 A047949 A075423

Adjacent sequences: A075299 A075300 A075301 this_sequence A075303 A075304 A075305

nonn,tabl

Antti Karttunen Sep 12 2002