login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

COMMENTS

a(A007583(n)) are the only terms with all 1s digits; the number of digits = 2n+1. - Bob Selcoe, Aug 21 2016

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.

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

Cf. A007583

Sequence in context: A278758 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 17:26 EST 2016. Contains 278755 sequences.