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

0,3

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

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A241816, A246591, A246592, A246594.

Sequence in context: A334666 A163380 A233569 * A256999 A331857 A073138

Adjacent sequences: A246590 A246591 A246592 * A246594 A246595 A246596

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 03 2014

Extensions

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

Status

approved