A238757 Lexicographically earliest sequence of distinct positive integers such that for any n>0 we have (a(n) AND n) = 0 (where AND stands for the bitwise AND operator).

2, 1, 4, 3, 8, 9, 16, 5, 6, 17, 20, 18, 32, 33, 48, 7, 10, 12, 36, 11, 34, 40, 64, 35, 38, 37, 68, 65, 66, 96, 128, 13, 14, 21, 24, 19, 26, 25, 72, 22, 70, 69, 80, 67, 82, 81, 144, 15, 74, 73, 76, 75, 130, 129, 136, 71, 132, 133, 192, 131, 194, 193, 256, 23

Offset: 1

Author

Paul Tek, Mar 05 2014

Keywords

• nonn

Comments

This is a permutation of the positive integers.

Apparently, a self-inverse permutation.

There are no fixed points.

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, Perl program for this sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A238758.

Programs

Perl

See Link section.

Python

from itertools import count, islice
def agen(): # generator of terms
    aset, mink = set(), 1
    for n in count(1):
        an = mink
        while an in aset or n&an: an += 1
        aset.add(an); yield an
        while mink in aset: mink += 1
print(list(islice(agen(), 64))) # Michael S. Branicky, Jun 22 2022