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A048647
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Write n in base 4, then replace each digit by its base 4 negative.
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16
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0, 3, 2, 1, 12, 15, 14, 13, 8, 11, 10, 9, 4, 7, 6, 5, 48, 51, 50, 49, 60, 63, 62, 61, 56, 59, 58, 57, 52, 55, 54, 53, 32, 35, 34, 33, 44, 47, 46, 45, 40, 43, 42, 41, 36, 39, 38, 37, 16, 19, 18, 17, 28, 31, 30, 29, 24, 27, 26, 25, 20, 23, 22, 21, 192, 195, 194, 193, 204, 207, 206
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OFFSET
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0,2
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COMMENTS
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The graph of a(n) on [ 1..4^k ] resembles a plane fractal of fractal dimension 1.
Self-inverse considered as a permutation of the positive integers.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..16383
J. W. Layman, View fractal-like graph
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = if n = 0 then 0 else 4*a(floor(n/4)) + if m = 0 then 0 else 4 - m, where m = n mod 4. - Reinhard Zumkeller, Apr 08 2013
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EXAMPLE
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a(15)=5, since 15 = 33(base 4) -> 11(base 4) = 5.
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MATHEMATICA
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Table[FromDigits[If[#==0, 0, 4-#]&/@IntegerDigits[n, 4], 4], {n, 0, 70}] (* Harvey P. Dale, Jul 23 2012 *)
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PROG
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(Haskell)
a048647 0 = 0
a048647 n = 4 * a048647 n' + if m == 0 then 0 else 4 - m
where (n', m) = divMod n 4
-- Reinhard Zumkeller, Apr 08 2013
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CROSSREFS
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Cf. A065256.
Cf. A007090.
Sequence in context: A092582 A213262 A068440 * A180190 A059438 A156628
Adjacent sequences: A048644 A048645 A048646 * A048648 A048649 A048650
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KEYWORD
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nonn,easy,nice,base
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu (7/5/99))
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STATUS
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approved
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