A061601 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.

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

Offset: 0

Author

Amarnath Murthy, May 19 2001

Keywords

• nonn
• base
• easy

Comments

A109002 and A178500 give record values and where they occur: A109002(n+1)=a(A178500(n)) and a(m)<A109002(n+1) for m<A178500(n). - Reinhard Zumkeller, May 28 2010

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

Examples

			a(7) = 2 = 10 - 1 -7. a(123) = 1000 -1 -123 = 876.
		

References

• Kjartan Poskitt, Murderous Maths: Numbers, The Key to the Universe, Scholastic Ltd, 2002. See p 159.

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..25000 (terms 0..1000 from Harry J. Smith)

Crossrefs

Cf. A035327, A171960.

Cf. A055120.

See A267193 for complement obverse of n.

Programs

Haskell

a061601 n = if n <= 9 then 9 - n else 10 * ad n' + 9 - d
            where (n',d) = divMod n 10
-- Reinhard Zumkeller, Feb 21 2014, Oct 04 2011

Maple

A061601 := proc(n)
        10^A055642(n)-1-n ;
end proc: # R. J. Mathar, Nov 30 2011

Mathematica

nineComplement[n_] := FromDigits[Table[9, {Length[IntegerDigits[n]]}] - IntegerDigits[n]]; Table[nineComplement[n], {n, 0, 71}] (* Alonso del Arte, Nov 30 2011 *)

PARI

A061601(n)=my(e=length(Str(n)));10^e-1 - n; \\ Joerg Arndt, Aug 28 2013

Python

def A061601(n):
    return 10**len(str(n))-1-n # Indranil Ghosh, Jan 30 2017

Formula

a(n) = if n<10 then 9 - n else 10*a([n/10]) + 9 - n mod 10. - Reinhard Zumkeller, Jan 20 2010

a(n) <= 9n - 1. - Charles R Greathouse IV, Nov 15 2022

Extensions

Corrected and extended by Matthew Conroy, Jan 19 2002