A073788 Numbers in base -7.

0, 1, 2, 3, 4, 5, 6, 160, 161, 162, 163, 164, 165, 166, 150, 151, 152, 153, 154, 155, 156, 140, 141, 142, 143, 144, 145, 146, 130, 131, 132, 133, 134, 135, 136, 120, 121, 122, 123, 124, 125, 126, 110, 111, 112, 113, 114, 115, 116, 100, 101, 102, 103, 104, 105

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. A007093, A039724, A073785, A007608, A073786, A073787, 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, 7], {n, 0, 60}]

Python

def A073788(n):
    s, q = '', n
    while q >= 7 or q < 0:
        q, r = divmod(q, -7)
        if r < 0:
            q += 1
            r += 7
        s += str(r)
    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016