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Numbers in base -7.
11

%I #9 Apr 09 2016 17:06:41

%S 0,1,2,3,4,5,6,160,161,162,163,164,165,166,150,151,152,153,154,155,

%T 156,140,141,142,143,144,145,146,130,131,132,133,134,135,136,120,121,

%U 122,123,124,125,126,110,111,112,113,114,115,116,100,101,102,103,104,105

%N Numbers in base -7.

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

%H Chai Wah Wu, <a href="/A073788/b073788.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Negabinary.html">Negabinary</a>

%H Prepared and presented by Matthew Szudzik of Wolfram Research, <a href="http://library.wolfram.com/conferences/devconf99/challenge/">A Mathematica programming contest</a>

%t 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}]

%o (Python)

%o def A073788(n):

%o s, q = '', n

%o while q >= 7 or q < 0:

%o q, r = divmod(q, -7)

%o if r < 0:

%o q += 1

%o r += 7

%o s += str(r)

%o return int(str(q)+s[::-1]) # _Chai Wah Wu_, Apr 09 2016

%Y Cf. A007093, A039724, A073785, A007608, A073786, A073787, A073789, A073790 & A039723.

%K base,easy,nonn

%O 0,3

%A _Robert G. Wilson v_, Aug 11 2002