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A039724
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Numbers in base -2.
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15
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0, 1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, 11110, 11111, 11100, 11101, 10010, 10011, 10000, 10001, 10110, 10111, 10100, 10101, 1101010, 1101011, 1101000, 1101001, 1101110, 1101111, 1101100, 1101101, 1100010, 1100011, 1100000, 1100001, 1100110, 1100111, 1100100
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 101.
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 189.
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LINKS
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William A. Tedeschi, Table of n, a(n) for n=0..10000
Joerg Arndt, Fxtbook, p. 58-59
Matthew Szudzik, A Mathematica programming contest
Eric Weisstein, Negabinary (MathWorld)
Wikipedia, Negative base
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EXAMPLE
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2 = 4+(-2)+0 = 110, 3 = 4+(-2)+1 = 111, ..., 6 = (16)+(-8)+0+(-2)+0 = 11010.
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MATHEMATICA
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ToNegaBases[ i_Integer, b_Integer ] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[ (#1 - Mod[ #1, b ])/-b &, i, #1 != 0 & ], b ] ] ] ]; Table[ ToNegaBases[ n, 2 ], {n, 0, 31} ]
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PROG
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(Haskell)
a039724 0 = 0
a039724 n = a039724 n' * 10 + m where
(n', m) = if r < 0 then (q + 1, r + 2) else (q, r)
where (q, r) = quotRem n (negate 2)
-- Reinhard Zumkeller, Jul 07 2012
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CROSSREFS
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Cf. A007088, A005351, A039723, A073785, A007608, A073786, A073787, A073788, A073789, A073790, A039723.
Cf. A212529 (negative numbers in base -2).
Sequence in context: A045884 A110736 A084292 * A008944 A106004 A113556
Adjacent sequences: A039721 A039722 A039723 * A039725 A039726 A039727
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KEYWORD
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base,nice,nonn,easy
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AUTHOR
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Robert Lozyniak (11(AT)onna.com)
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EXTENSIONS
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More terms from Eric W. Weisstein.
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STATUS
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approved
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