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

1,11

Comments

The binary reverse of a number is given by A030101.

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Index entries for sequences related to binary expansion of n

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.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A138066 A173189 A115595 * A381535 A187553 A003621

Adjacent sequences: A342120 A342121 A342122 * A342124 A342125 A342126

Keyword

nonn,base,look,easy

Author

Rémy Sigrist, Feb 28 2021

Status

approved