A073786 Numbers in base -5.

0, 1, 2, 3, 4, 140, 141, 142, 143, 144, 130, 131, 132, 133, 134, 120, 121, 122, 123, 124, 110, 111, 112, 113, 114, 100, 101, 102, 103, 104, 240, 241, 242, 243, 244, 230, 231, 232, 233, 234, 220, 221, 222, 223, 224, 210, 211, 212, 213, 214, 200, 201, 202, 203

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. A007091, A039724, A073785, A007608, A073787, A073788, A073789, A073790 & A039723.

Programs

Mathematica

ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]]; Table[ ToNegaBases[n, 5], {n, 0, 55}]

Python

def A073786(n):
    s, q = '', n
    while q >= 5 or q < 0:
        q, r = divmod(q, -5)
        if r < 0:
            q += 1
            r += 5
        s += str(r)
    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016