A342121 -id:A342121 - cp's OEIS frontend

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

Rémy Sigrist, Feb 28 2021

The binary reverse of a number is given by A030101.

This sequence is the analog of A103168 for the binary base.

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

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

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

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

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

def A342122(n): return int(bin(n)[:1:-1],2) % n if n > 0 else 0 # Chai Wah Wu, Mar 01 2021

a(n) = A030101(n) mod n.
a(n) < n.
a(n) = 0 iff n is a binary palindrome (A006995).

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

Original entry on oeis.org

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

Rémy Sigrist, Feb 28 2021

The binary reverse of a number is given by A030101.

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

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

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

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

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

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

a(n) = n mod A030101(n).
a(n) <= n with equality iff n belongs to A161601.
a(n) = 0 iff n belongs to A057890.

cp's OEIS Frontend

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

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