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

0,3

Comments

A030101 gives the binary reversal of a number.

All positive terms belong to A209492.

This sequence is nondecreasing.

Links

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

Formula

a(n) <= n + 1.

Example

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

Prog

(PARI) { base = 2; k = 0; r = 0; for (n=0, 67, while (r<n, r = fromdigits(Vecrev(digits(k++, base)), base); ); print1 (k ", ")) }
(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

Crossrefs

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

Sequence in context: A177691 A206913 A117767 * A293701 A296063 A127630

Adjacent sequences: A340833 A340834 A340835 * A340837 A340838 A340839

Keyword

nonn,base

Author

Rémy Sigrist, Mar 13 2021

Status

approved