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A061601
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9's complement of n: a(n) = 10^d - 1 - n where d is the number of digits in n. If a is a digit in n replace it with 9 - a.
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27
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9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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If n is divisible by 3, so is a(n). The same goes for 9. - Alonso del Arte, Dec 01 2011
For n > 0, a(n-1) consists of the A055642(n) least significant digits of the 10-adic integer -n. - Stefano Spezia, Jan 21 2021
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REFERENCES
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Kjartan Poskitt, Murderous Maths: Numbers, The Key to the Universe, Scholastic Ltd, 2002. See p 159.
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LINKS
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FORMULA
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a(n) = if n<10 then 9 - n else 10*a([n/10]) + 9 - n mod 10. - Reinhard Zumkeller, Jan 20 2010
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EXAMPLE
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a(7) = 2 = 10 - 1 -7. a(123) = 1000 -1 -123 = 876.
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MAPLE
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MATHEMATICA
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nineComplement[n_] := FromDigits[Table[9, {Length[IntegerDigits[n]]}] - IntegerDigits[n]]; Table[nineComplement[n], {n, 0, 71}] (* Alonso del Arte, Nov 30 2011 *)
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PROG
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(PARI) g(n) = for(x=0, n, ln=length(Str(x)); y=10^ln-1 - x; print1(y", ")) \\ Cino Hilliard, Mar 11 2006
(PARI) for (n=0, 1000, ln=length(Str(n)); write("b061601.txt", n, " ", 10^ln - 1 - n) ) \\ Harry J. Smith, Jul 25 2009
(Haskell)
a061601 n = if n <= 9 then 9 - n else 10 * ad n' + 9 - d
where (n', d) = divMod n 10
(Python)
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CROSSREFS
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See A267193 for complement obverse of n.
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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