A073790 Numbers in base -9.

0, 1, 2, 3, 4, 5, 6, 7, 8, 180, 181, 182, 183, 184, 185, 186, 187, 188, 170, 171, 172, 173, 174, 175, 176, 177, 178, 160, 161, 162, 163, 164, 165, 166, 167, 168, 150, 151, 152, 153, 154, 155, 156, 157, 158, 140, 141, 142, 143, 144, 145, 146, 147, 148, 130, 131

Offset: 0

Author

Robert G. Wilson v, Aug 11 2002

Keywords

• base
• easy
• nonn

References

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Negabinary
• Prepared and presented by Matthew Szudzik of Wolfram Research, A Mathematica programming contest

Crossrefs

Cf. A007095, A039724, A073785, A007608, A073786, A073787, A073788, A073789 & A039723.

Programs

Mathematica

ToNegaBases[i_Integer, b_Integer] := FromDigits@ Rest@ Reverse@ Mod[ NestWhileList[(# - Mod[ #, b])/-b &, i, # != 0 &], b]; Table[ ToNegaBases[n, 9], {n, 0, 60}]

Python

def A073790(n):
    s, q = '', n
    while q >= 9 or q < 0:
        q, r = divmod(q, -9)
        if r < 0:
            q += 1
            r += 9
        s += str(r)
    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016