A246591 Smallest number that can be obtained by swapping 2 bits in the binary expansion of n.

0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 5, 7, 7, 15, 1, 3, 3, 7, 5, 7, 7, 15, 9, 11, 11, 15, 13, 15, 15, 31, 1, 3, 3, 7, 5, 7, 7, 15, 9, 11, 11, 15, 13, 15, 15, 31, 17, 19, 19, 23, 21, 23, 23, 31, 25, 27, 27, 31, 29, 31, 31, 63, 1, 3, 3, 7, 5, 7, 7, 15, 9, 11, 11

Offset: 0

Author

N. J. A. Sloane, Sep 03 2014

Keywords

• nonn
• base

Comments

Swap the first 1 with the last 0 in the binary expansion of n.

Examples

			If n = 12 = 1100_2 then a(12) = 0101_2 = 5.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..8190

Crossrefs

Cf. A241816, A246592, A246593, A246594.

Programs

Python

from itertools import combinations
def A246591(n):
    if n <= 1:
        return n
    else:
        s = bin(n)[2:]
        l = len(s)
        y = 2**l-1
        for i in combinations(range(l), 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

def A246591(n):
    s = bin(n)[2:]
    s2 = s.rstrip('1')
    return(int(s2[1:-1]+'1'+s[len(s2):], 2) if (len(s2) > 0 and n > 1) else n)
# Chai Wah Wu, Sep 08 2014

Extensions

More terms from Alois P. Heinz, Sep 03 2014