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A342121
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a(n) is the remainder when the larger of n and its binary reverse is divided by the smaller.
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3
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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
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OFFSET
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1,11
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COMMENTS
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The binary reverse of a number is given by A030101.
This sequence is the analog of A061467 for the binary base.
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LINKS
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FORMULA
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a(n) < n.
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EXAMPLE
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For n = 43,
- the binary reverse of 43 ("101011" in binary) is 53 ("110101" in binary),
- so a(43) = 53 mod 43 = 10.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n, base=2) = { my (r=fromdigits(Vecrev(digits(n, base)), base)); max(n, r) % min(n, r) }
(Python)
a, b = sorted([n, int(bin(n)[:1:-1], 2)])
return b % a if n > 0 else 0 # Chai Wah Wu, Mar 01 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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