A246866 Bitmasks that can be used to generate a sequence of all positive integers up to 2^n.

3, 6, 12, 20, 48, 96, 184, 272, 576, 1280, 3232, 6912, 13568, 24576, 46080, 73728, 132096, 466944, 589824, 1310720, 3145728, 4194304, 14155776, 18874368, 59244544, 119537664, 150994944, 335544320, 847249408, 1207959552, 2734686208

Offset

2,1

Comments

The sequence skips around in a simple pseudo-random order hitting each number from 1 to 2^n exactly once, which makes it suitable for use in e.g. a dissolve-style pixel graphics effect.

JavaScript code to generate all numbers from 1 to 2^n using XOR_MASK, an element of this sequence:

var i = 1; do { i = (i >> 1) ^ (i & 1 ? XOR_MASK : 0); } while (i != 1);

First few numbers of this sequence in hexadecimal, for searchability: 0x03, 0x06, 0x0C, 0x14, 0x30, 0x60, 0xB8, 0x0110, 0x0240, ...

References

Andrew S. Glassner, Graphics Gems, Academic Press, 1990, pages 221-232.

Links

Table of n, a(n) for n=2..32.

Mactech.com, Source code for old Macintosh project (see dissMask.c)

Ticalc.org, Source code for TI-89 project (see file dissolve.c)

Ticalc.org, TI-89 project programmer's project page

Crossrefs

Sequence in context: A028924 A034738 A054064 * A053479 A290768 A070333

Adjacent sequences: A246863 A246864 A246865 * A246867 A246868 A246869

Keyword

more,nonn

Author

James Nylen, Sep 05 2014

Status

approved