A347347 If n is odd, a(n) is the smallest positive integer that is a palindrome when represented in binary, and is made by appending some number (zero or more) of binary digits on the left of n's binary representation. If n is even, then a(n) = 0.

1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 27, 0, 45, 0, 15, 0, 17, 0, 51, 0, 21, 0, 119, 0, 153, 0, 27, 0, 93, 0, 31, 0, 33, 0, 99, 0, 165, 0, 231, 0, 297, 0, 107, 0, 45, 0, 495, 0, 561, 0, 51, 0, 693, 0, 119, 0, 313, 0, 443, 0, 189, 0, 63, 0, 65, 0, 195, 0, 325, 0, 455, 0

Offset: 1

Author

Chai Wah Wu, Aug 27 2021

Keywords

• nonn
• base
• look

Comments

Base-2 analog of A347346.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030101, A161501, A347346.

Programs

Python

def A347347(n):
    if n % 2 == 0:
        return 0
    s = bin(n)[2:]
    if s == s[::-1]:
        return n
    for i in range(1,len(s)):
        if s[:-i]== s[-i-1::-1]:
            return int(s[:-i-1:-1]+s,2)

Formula

If n is odd, then a(n) = A161501(A030101(i)).