A342123 a(n) is the remainder when n is divided by its binary reverse.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 2, 0, 0, 0, 0, 0, 19, 0, 0, 9, 23, 0, 6, 4, 0, 0, 6, 0, 0, 0, 0, 0, 35, 0, 37, 13, 39, 0, 4, 0, 43, 5, 0, 17, 47, 0, 14, 12, 0, 8, 10, 0, 55, 0, 18, 12, 4, 0, 14, 0, 0, 0, 0, 0, 67, 0, 69, 21, 71, 0, 0, 33, 75, 1, 77, 21

Offset: 1

Author

Rémy Sigrist, Feb 28 2021

Keywords

• nonn
• base
• look
• easy

Comments

The binary reverse of a number is given by A030101.

This sequence is the analog of A071955 for the binary base.

Examples

			For n = 43,
- the binary reverse of 43 ("101011" in binary) is 53 ("110101" in binary),
- so a(43) = 43 mod 53 = 43.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A030101, A057890, A071955, A161601, A342121, A342122.

Programs

PARI

a(n, base=2) = { my (r=fromdigits(Vecrev(digits(n, base)), base)); n%r }

Python

def A342123(n): return n % int(bin(n)[:1:-1],2) if n > 0 else 0 # Chai Wah Wu, Mar 01 2021

Formula

a(n) = n mod A030101(n).

a(n) <= n with equality iff n belongs to A161601.

a(n) = 0 iff n belongs to A057890.