A161501 -id:A161501 - cp's OEIS frontend

A161502 a(n) is the smallest number of binary digits that when appended to the right side of the binary representation of n, forms a binary palindrome.

0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 2, 2, 1, 3, 0, 1, 0, 2, 3, 3, 0, 1, 2, 2, 1, 2, 0, 3, 2, 4, 0, 1, 0, 3, 4, 1, 3, 2, 3, 3, 2, 1, 4, 4, 0, 1, 2, 2, 1, 3, 0, 4, 1, 2, 3, 3, 2, 3, 1, 4, 3, 5, 0, 1, 0, 4, 5, 2, 4, 3, 4, 4, 0, 2, 5, 1, 4, 2, 3, 3, 2, 1, 5, 5, 0, 3, 4, 4, 3, 4, 2, 5, 0, 1, 2, 2, 1, 4, 0, 2, 4, 3, 4, 4, 3

Offset: 1

Leroy Quet, Jun 11 2009

			11 (decimal) in binary is 1011. Appending 01 to the right side of 1011 forms the binary palindrome 101101, which is 45 in decimal. Since two binary digits is the smallest number of digits that need to be appended on the right side of binary n to form a palindrome, then a(11) = 2. (Note that 45 is not the smallest positive number that when represented in binary is a palindrome and contains 1011 as a substring. That would instead be 11011 {binary} = 27 {decimal}.)

Cf. A145800, A161501.

def A161502(n):
    s = bin(n)[2:]
    if s == s[::-1]:
        return 0
    for i in range(1,len(s)):
        if s[i:] == s[-1:i-1:-1]:
            return i # Chai Wah Wu, Aug 27 2021

More terms from Sean A. Irvine, Sep 27 2009

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.

Original entry on oeis.org

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

Chai Wah Wu, Aug 27 2021

Base-2 analog of A347346.

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

Cf. A030101, A161501, A347346.

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)

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

cp's OEIS Frontend

A161502 a(n) is the smallest number of binary digits that when appended to the right side of the binary representation of n, forms a binary palindrome.

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

Extensions