A342121 a(n) is the remainder when the larger of n and its binary reverse is divided by the smaller.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 9, 6, 0, 6, 4, 0, 0, 6, 0, 0, 0, 0, 0, 14, 0, 4, 13, 18, 0, 4, 0, 10, 5, 0, 17, 14, 0, 14, 12, 0, 8, 10, 0, 4, 0, 18, 12, 4, 0, 14, 0, 0, 0, 0, 0, 30, 0, 12, 21, 42, 0, 0, 33, 30, 1, 12, 21, 42, 0

Offset

1,11

Comments

The binary reverse of a number is given by A030101.

This sequence is the analog of A061467 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) = max(n, A030101(n)) mod min(n, A030101(n)).

a(n) = min(A342122(n), A342123(n)).

a(n) < n.

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) = 53 mod 43 = 10.

Mathematica

rbr[n_]:=Module[{r=IntegerReverse[n, 2]}, If[r>n, Mod[r, n], Mod[n, r]]]; Array[rbr, 100] (* Harvey P. Dale, Mar 18 2023 *)

Prog

(PARI) a(n, base=2) = { my (r=fromdigits(Vecrev(digits(n, base)), base)); max(n, r) % min(n, r) }
(Python)
def A342121(n):
    a, b = sorted([n, int(bin(n)[:1:-1], 2)])
    return b % a if n > 0 else 0 # Chai Wah Wu, Mar 01 2021

Crossrefs

Cf. A030101, A057890, A061467, A342122, A342123..

Sequence in context: A331293 A335379 A358061 * A258764 A109083 A256812

Adjacent sequences: A342118 A342119 A342120 * A342122 A342123 A342124

Keyword

nonn,base,look,easy

Author

Rémy Sigrist, Feb 28 2021

Status

approved