A039723 Numbers in base -10.

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

Offset: 0

Author

Robert Lozyniak (11(AT)onna.com)

Keywords

• base
• easy
• nonn

Examples

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

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

Crossrefs

Nonnegative numbers in negative bases: this sequence (b=-10), A039724 (b=-2), A073785 (b=-3), A007608 (b=-4), A073786 (b=-5), A073787 (b=-6), A073788 (b=-7), A073789 (b=-8), A073790 (b=-9).

Cf. A051022.

Cf. A305238: negative numbers in base -10.

Programs

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

Mathematica

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

PARI

A039723 = base(n, b=-10) = if(n, base(n\b, b)*10 + n%b, 0) \\ M. F. Hasler, Oct 16 2018 [Corrected by Jianing Song, Oct 21 2018]

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