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A342121 a(n) is the remainder when the larger of n and its binary reverse is divided by the smaller. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A331293 A335379 A358061 * A258764 A109083 A256812
KEYWORD
nonn,base,look,easy
AUTHOR
Rémy Sigrist, Feb 28 2021
STATUS
approved

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Last modified March 28 13:19 EDT 2024. Contains 371254 sequences. (Running on oeis4.)