A071955 -id:A071955 - cp's OEIS frontend

A103168 a(n) is the remainder when (n written backwards) is divided by n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 9, 5, 13, 6, 13, 3, 9, 15, 2, 12, 0, 9, 18, 2, 10, 18, 26, 5, 3, 13, 23, 0, 9, 18, 27, 36, 7, 15, 4, 14, 24, 34, 0, 9, 18, 27, 36, 45, 5, 15, 25, 35, 45, 0, 9, 18, 27, 36, 6, 16, 26, 36, 46, 56, 0, 9, 18, 27, 7, 17, 27, 37, 47, 57, 67, 0, 9, 18, 8, 18, 28, 38

Offset: 1

Labos Elemer, Jan 28 2005

			a(n) = 0 for palindromic numbers.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A071955, A103166-A103169, A002113, A071590.

rd[x_]:=FromDigits[Reverse[IntegerDigits[x]]] Table[Mod[rd[n], n], {n, 1, 256}]
Table[Mod[IntegerReverse[n],n],{n,90}] (* Harvey P. Dale, Jun 20 2025 *)

a(n, base=10) = my (r=fromdigits(Vecrev(digits(n, base)), base)); r%n \\ Rémy Sigrist, Apr 05 2020

def a(n): return int(str(n)[::-1])%n
print([a(n) for n in range(1, 84)]) # Michael S. Branicky, Dec 12 2021

Definition corrected by N. J. A. Sloane, Jul 14 2007

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

A103168 a(n) is the remainder when (n written backwards) is divided by n.

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