|
%I #48 Nov 15 2022 14:28:46
%S 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,
%T 73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,
%U 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28
%N 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.
%C 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
%C If n is divisible by 3, so is a(n). The same goes for 9. - _Alonso del Arte_, Dec 01 2011
%C 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
%D Kjartan Poskitt, Murderous Maths: Numbers, The Key to the Universe, Scholastic Ltd, 2002. See p 159.
%H Indranil Ghosh, <a href="/A061601/b061601.txt">Table of n, a(n) for n = 0..25000</a> (terms 0..1000 from Harry J. Smith)
%F a(n) = if n<10 then 9 - n else 10*a([n/10]) + 9 - n mod 10. - _Reinhard Zumkeller_, Jan 20 2010
%F a(n) <= 9n - 1. - _Charles R Greathouse IV_, Nov 15 2022
%e a(7) = 2 = 10 - 1 -7. a(123) = 1000 -1 -123 = 876.
%p A061601 := proc(n)
%p 10^A055642(n)-1-n ;
%p end proc: # _R. J. Mathar_, Nov 30 2011
%t nineComplement[n_] := FromDigits[Table[9, {Length[IntegerDigits[n]]}] - IntegerDigits[n]]; Table[nineComplement[n], {n, 0, 71}] (* _Alonso del Arte_, Nov 30 2011 *)
%o (PARI) g(n) = for(x=0,n,ln=length(Str(x));y=10^ln-1 - x;print1(y",")) \\ _Cino Hilliard_, Mar 11 2006
%o (PARI) for (n=0, 1000, ln=length(Str(n)); write("b061601.txt", n, " ", 10^ln - 1 - n) ) \\ _Harry J. Smith_, Jul 25 2009
%o (PARI) A061601(n)=my(e=length(Str(n)));10^e-1 - n; \\ _Joerg Arndt_, Aug 28 2013
%o (Haskell)
%o a061601 n = if n <= 9 then 9 - n else 10 * ad n' + 9 - d
%o where (n',d) = divMod n 10
%o -- _Reinhard Zumkeller_, Feb 21 2014, Oct 04 2011
%o (Python)
%o def A061601(n):
%o return 10**len(str(n))-1-n # _Indranil Ghosh_, Jan 30 2017
%Y Cf. A035327, A171960.
%Y Cf. A055120.
%Y See A267193 for complement obverse of n.
%K nonn,base,easy
%O 0,1
%A _Amarnath Murthy_, May 19 2001
%E Corrected and extended by _Matthew Conroy_, Jan 19 2002
|
