A342122 -id:A342122 - cp's OEIS frontend

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

Rémy Sigrist, Feb 28 2021

The binary reverse of a number is given by A030101.

This sequence is the analog of A061467 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. A030101, A057890, A061467, A342122, A342123..

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 *)

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

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

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.

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

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

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