A246593 a(n)=n for n <= 2; for n >= 3, a(n) = largest number that can be obtained by swapping two bits in the binary expansion of n.

0, 1, 2, 3, 4, 6, 6, 7, 8, 12, 12, 14, 12, 14, 14, 15, 16, 24, 24, 26, 24, 28, 28, 30, 24, 28, 28, 30, 28, 30, 30, 31, 32, 48, 48, 50, 48, 52, 52, 54, 48, 56, 56, 58, 56, 60, 60, 62, 48, 56, 56, 58, 56, 60, 60, 62, 56, 60, 60, 62, 60, 62, 62, 63, 64, 96, 96

Offset: 0

Author

N. J. A. Sloane, Sep 03 2014

Keywords

• nonn
• base

Comments

In both this sequence and A246594 you are not allowed to touch any of the invisible 0's before the leading 1.

Swap first 0 with last 1 in the binary expansion of n or return n if no such swap is possible. - Chai Wah Wu, Sep 08 2014

Examples

			If n = 17 = 10001_2 then a(17) = 11000_2 = 24.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A241816, A246591, A246592, A246594.

Programs

Python

from itertools import combinations
def A246593(n):
    if n <= 1:
        return n
    else:
        s, y = bin(n)[2:], n
        for i in combinations(range(len(s)),2):
            s2 = int(s[:i[0]]+s[i[1]]+s[i[0]+1:i[1]]+s[i[0]]+s[i[1]+1:],2)
            if s2 > y:
                y = s2
        return y
# Chai Wah Wu, Sep 05 2014

Python

# implement algorithm in comment
def A246593(n):
    s = bin(n)[2:]
    s2 = s.rstrip('0')
    s3 = s2.lstrip('1')
    return(int(s2[:-len(s3)]+'1'+s3[1:-1]+'0'+s[len(s2):],2) if (len(s3) > 0 and n > 1) else n)
# Chai Wah Wu, Sep 08 2014

Extensions

Corrected definition and more terms from Alois P. Heinz, Sep 04 2014