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A007608 Nonnegative integers in base -4.
(Formerly M0926)
15
0, 1, 2, 3, 130, 131, 132, 133, 120, 121, 122, 123, 110, 111, 112, 113, 100, 101, 102, 103, 230, 231, 232, 233, 220, 221, 222, 223, 210, 211, 212, 213, 200, 201, 202, 203, 330, 331, 332, 333, 320, 321, 322, 323, 310, 311, 312, 313, 300, 301, 302, 303, 13030 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The base 2i representation (quater-imaginary representation) of nonnegative integers is obtained by interleaving with zeros, cf. A212494.

More precisely, a(n) is the number n written in base -4; numbers [which represent some nonnegative integer] in base -4 are 0, 1, 2, 3, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133,... - M. F. Hasler, May 20 2012

REFERENCES

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 189.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Joerg Arndt, Table of n, a(n) for n = 0..1000

Matthew Szudzik, A Mathematica programming contest.

Eric Weisstein, Negabinary (MathWorld).

Wikipedia, Negative base

MATHEMATICA

ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]]; Table[ ToNegaBases[n, 4], {n, 0, 55}]

PROG

(PARI) A007608(n, s="")={until(!n\=-4, s=Str(n%-4, s)); eval(s)}  \\ M. F. Hasler, May 20 2012

(Haskell)

a007608 0 = 0

a007608 n = a007608 n' * 10 + m where

   (n', m) = if r < 0 then (q + 1, r + 4) else (q, r)

             where (q, r) = quotRem n (negate 4)

-- Reinhard Zumkeller, Jul 15 2012

(Python)

def A007608(n):

    s, q = '', n

    while q >= 4 or q < 0:

        q, r = divmod(q, -4)

        if r < 0:

            q += 1

            r += 4

        s += str(r)

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

CROSSREFS

Cf. A007090, A039724, A073785, A073786, A073787, A073788, A073789, A073790 & A039723.

Cf. A212526 (Negative integers in base -4).

Sequence in context: A004865 A006286 A139129 * A010343 A118169 A066908

Adjacent sequences:  A007605 A007606 A007607 * A007609 A007610 A007611

KEYWORD

base,nice,easy,nonn

AUTHOR

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

STATUS

approved

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Last modified November 18 18:46 EST 2017. Contains 294894 sequences.