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A073785 Numbers in base -3. 11
0, 1, 2, 120, 121, 122, 110, 111, 112, 100, 101, 102, 220, 221, 222, 210, 211, 212, 200, 201, 202, 12020, 12021, 12022, 12010, 12011, 12012, 12000, 12001, 12002, 12120, 12121, 12122, 12110, 12111, 12112, 12100, 12101, 12102, 12220, 12221, 12222 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 189.
LINKS
Jaime Rangel-Mondragon, Negabinary Numbers to Decimal
Eric Weisstein's World of Mathematics, Negabinary
Wikipedia, Negative base
MATHEMATICA
ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]]; Table[ ToNegaBases[n, 3], {n, 0, 45}]
PROG
(Haskell)
a073785 0 = 0
a073785 n = a073785 n' * 10 + m where
(n', m) = if r < 0 then (q + 1, r + 3) else (q, r)
where (q, r) = quotRem n (negate 3)
-- Reinhard Zumkeller, Jul 07 2012
(Python)
def A073785(n):
s, q = '', n
while q >= 3 or q < 0:
q, r = divmod(q, -3)
if r < 0:
q += 1
r += 3
s += str(r)
return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016
(PARI) A073785 = base(n, b=-3) = if(n, base(n\b, b)*10 + n%b, 0) \\ Jianing Song, Oct 20 2018
CROSSREFS
Cf. A007089.
Nonnegative numbers in negative bases: A039723 (b=-10), A039724 (b=-2), this sequence (b=-3), A007608 (b=-4), A073786 (b=-5), A073787 (b=-6), A073788 (b=-7), A073789 (b=-8), A073790 (b=-9).
Cf. A320636 (negative numbers in base -3).
Sequence in context: A243512 A165163 A153658 * A102355 A206355 A360607
KEYWORD
base,easy,nonn
AUTHOR
Robert G. Wilson v, Aug 11 2002
STATUS
approved

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Last modified March 19 03:20 EDT 2024. Contains 370952 sequences. (Running on oeis4.)