A342122 a(n) is the remainder when the binary reverse of n is divided by n.

0, 1, 0, 1, 0, 3, 0, 1, 0, 5, 2, 3, 11, 7, 0, 1, 0, 9, 6, 5, 0, 13, 6, 3, 19, 11, 0, 7, 23, 15, 0, 1, 0, 17, 14, 9, 4, 25, 18, 5, 37, 21, 10, 13, 0, 29, 14, 3, 35, 19, 0, 11, 43, 27, 4, 7, 39, 23, 55, 15, 47, 31, 0, 1, 0, 33, 30, 17, 12, 49, 42, 9, 0, 41, 30

Offset

1,6

Comments

The binary reverse of a number is given by A030101.

This sequence is the analog of A103168 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) = A030101(n) mod n.

a(n) < n.

a(n) = 0 iff n is a binary palindrome (A006995).

Example

For n = 43,
- the binary reverse of 43 ("101011" in binary) is 53 ("110101" in binary),
- so a(43) = 53 mod 43 = 10.

Mathematica

Table[Mod[FromDigits[Reverse[IntegerDigits[n, 2]], 2], n], {n, 80}] (* Harvey P. Dale, Mar 01 2023 *)

Prog

(PARI) a(n, base=2) = { my (r=fromdigits(Vecrev(digits(n, base)), base)); r%n }
(Python)
def A342122(n): return int(bin(n)[:1:-1], 2) % n if n > 0 else 0 # Chai Wah Wu, Mar 01 2021

Crossrefs

Cf. A006995, A030101, A103168, A342121, A342123.

Sequence in context: A178921 A046665 A100574 * A056100 A141665 A136689

Adjacent sequences: A342119 A342120 A342121 * A342123 A342124 A342125

Keyword

nonn,base,look,easy

Author

Rémy Sigrist, Feb 28 2021

Status

approved