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A039723 Numbers in base -10. 12
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 150, 151, 152, 153, 154, 155 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Prepared and presented by Matthew Szudzik of Wolfram Research, A Mathematica programming contest

Eric Weisstein's World of Mathematics, Negadecimal

Eric Weisstein's World of Mathematics, Negabinary

Wikipedia, Negative base

EXAMPLE

Decimal 25 is "185" in base -10 because 100-80+5=25.

MATHEMATICA

ToNegaBases[i_Integer, b_Integer] := FromDigits@ Rest@ Reverse@ Mod[ NestWhileList[(# - Mod[ #, b])/-b &, i, # != 0 &], b]

PROG

(Haskell)

a039723 0 = 0

a039723 n = a039723 n' * 10 + m where

   (n', m) = if r < 0 then (q + 1, r + 10) else qr where

            qr@(q, r) = quotRem n (negate 10)

-- Reinhard Zumkeller, Apr 20 2011

(Python)

def A039723(n):

    s, q = '', n

    while q >= 10 or q < 0:

        q, r = divmod(q, -10)

        if r < 0:

            q += 1

            r += 10

        s += str(r)

    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 10 2016

CROSSREFS

Cf. A001477, A039724, A073785, A007608, A073786, A073787, A073788, A073789 & A073790.

Cf. A051022.

Sequence in context: A005188 A032569 A254960 * A002998 A061276 A249515

Adjacent sequences:  A039720 A039721 A039722 * A039724 A039725 A039726

KEYWORD

base,easy,nonn

AUTHOR

Robert Lozyniak (11(AT)onna.com)

STATUS

approved

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Last modified December 8 02:07 EST 2016. Contains 278902 sequences.