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A039724 Numbers in base -2. 25
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)
OFFSET

0,3

REFERENCES

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.

LINKS

William A. Tedeschi, Table of n, a(n) for n=0..10000

Joerg Arndt, Matters Computational (The Fxtbook), p. 58-59

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Matthew Szudzik, A Mathematica programming contest

Eric Weisstein, Negabinary (MathWorld)

Wikipedia, Negative base

FORMULA

G.f. g(x) satisfies g(x) = (x + 10 x^2 + 11 x^3)/(1-x^4) + 100(1+x+x^2+x^3) g(x^4)/x^2. - Robert Israel, Feb 24 2016

EXAMPLE

2 = 4+(-2)+0 = 110, 3 = 4+(-2)+1 = 111, ..., 6 = (16)+(-8)+0+(-2)+0 = 11010.

MAPLE

f:= proc(n) option remember; 10*floor((n mod 4)/2) + (n mod 2) + 100*procname(round(n/4)) end proc:

f(0):= 0:

seq(f(i), i=0..100); # Robert Israel, Feb 24 2016

MATHEMATICA

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} ]

PROG

(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

(Python)

def A039724(n):

    s, q = '', n

    while q >= 2 or q < 0:

        q, r = divmod(q, -2)

        if r < 0:

            q += 1

            r += 2

        s += str(r)

    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016

CROSSREFS

Cf. A007088, A005351, A039723, A073785, A007608, A073786, A073787, A073788, A073789, A073790, A039723.

Cf. A212529 (negative numbers in base -2).

Sequence in context: A266849 A266979 A267138 * A008944 A106004 A113556

Adjacent sequences:  A039721 A039722 A039723 * A039725 A039726 A039727

KEYWORD

base,nice,nonn,easy

AUTHOR

Robert Lozyniak (11(AT)onna.com)

EXTENSIONS

More terms from Eric W. Weisstein

STATUS

approved

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Last modified April 30 18:41 EDT 2016. Contains 272242 sequences.