A340836 - OEIS

%I #48 Mar 14 2021 14:26:31

%S 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,

%T 23,23,23,23,31,31,33,33,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,

%U 35,39,39,39,39,39,39,39,39,47,47,47,47,63,63,65,65,67,67

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

%C A030101 gives the binary reversal of a number.

%C All positive terms belong to A209492.

%C This sequence is nondecreasing.

%H Rémy Sigrist, <a href="/A340836/b340836.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) <= n + 1.

%e For n = 8:

%e - A030101(k) < 8 for any k <= 8,

%e - A030101(9) = 9 >= 8,

%e - so a(8) = 9.

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

%o (Python)

%o def A340836(n):

%o     if n == 0:

%o         return 0

%o     s = bin(n)[2:]

%o     i = s.find('0')

%o     if i == -1:

%o         return n

%o     s1, s2 = s[:i+1], s[i+1:]

%o     if s2 == '':

%o         return n+1

%o     if int(s2) <= 1:

%o         return int('1'+s2[-2::-1]+s1[::-1],2)

%o     else:

%o         return int('1'+'0'*(len(s2)-1)+bin(int(s1,2)+1)[:1:-1],2) # _Chai Wah Wu_, Mar 14 2021

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

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Mar 13 2021