A353733 a(0)=0, a(1)=1; for k >= 1, a(2*k+1) and a(2*k+2) are the two smallest numbers not yet in the sequence whose binary expansions have no 1's in common with the binary expansion of a(k).

0, 1, 2, 4, 6, 5, 8, 3, 9, 16, 17, 10, 18, 7, 19, 12, 20, 22, 32, 11, 13, 14, 34, 21, 33, 36, 37, 24, 40, 44, 64, 35, 48, 41, 42, 65, 72, 15, 23, 52, 68, 50, 66, 49, 80, 25, 28, 74, 96, 26, 30, 27, 67, 82, 88, 38, 39, 69, 70, 81, 83, 29, 31, 76, 84, 71, 73, 86

Offset: 0

Author

N. J. A. Sloane, May 17 2022

Keywords

• nonn
• look

Comments

A variant of A352808.

This is a permutation of the nonnegative numbers (the proof is similar to that for A352808).

Examples

			For k=2, after a(2) = 2 = 10_2, we get a(5) = 5 = 101_2 and a(6) = 8 = 1000_2 since 101_2, 1000_2 have no 1's in common with 10_2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A352808.

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    alst = [0, 1]; aset = {0, 1}; yield from alst
    mink = 2
    for n in count(2):
        ahalf, k = alst[(n-1)//2], mink
        while k in aset or k&ahalf: k += 1
        alst.append(k); aset.add(k); yield k
        while mink in aset: mink += 1
print(list(islice(agen(), 68))) # Michael S. Branicky, May 17 2022

Extensions

More terms from Michael S. Branicky, May 17 2022