A340836 a(n) is the least k such that the binary reversal of k is greater than or equal to n.

0, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 11, 11, 15, 15, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 31, 31, 33, 33, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 39, 39, 39, 39, 39, 39, 39, 39, 47, 47, 47, 47, 63, 63, 65, 65, 67, 67

Offset: 0

Author

Rémy Sigrist, Mar 13 2021

Keywords

• nonn
• base

Comments

A030101 gives the binary reversal of a number.

All positive terms belong to A209492.

This sequence is nondecreasing.

Examples

			For n = 8:
- A030101(k) < 8 for any k <= 8,
- A030101(9) = 9 >= 8,
- so a(8) = 9.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A030101, A209492, A340835 (decimal analog).

Programs

PARI

{ base = 2; k = 0; r = 0; for (n=0, 67, while (r
				

Python

def A340836(n):
    if n == 0:
        return 0
    s = bin(n)[2:]
    i = s.find('0')
    if i == -1:
        return n
    s1, s2 = s[:i+1], s[i+1:]
    if s2 == '':
        return n+1
    if int(s2) <= 1:
        return int('1'+s2[-2::-1]+s1[::-1],2)
    else:
        return int('1'+'0'*(len(s2)-1)+bin(int(s1,2)+1)[:1:-1],2) # Chai Wah Wu, Mar 14 2021

Formula

a(n) <= n + 1.