A109002 -id:A109002 - cp's OEIS frontend

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

Amarnath Murthy, May 19 2001

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

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

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

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

Cf. A035327, A171960.
Cf. A055120.
See A267193 for complement obverse of n.

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

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

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

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

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

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

Corrected and extended by Matthew Conroy, Jan 19 2002

A178500 a(n) = 10^n * signum(n).

Original entry on oeis.org

0, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000, 100000000000000000000

Offset: 0

Reinhard Zumkeller, May 28 2010

a(n-1) is the minimum difference between an n-digit number (written in base 10, nonzero leading digit) and the product of its digits. For n > 1, it is also a number meeting that bound. See A070565. - Devin Akman, Apr 17 2019

Michael De Vlieger, Table of n, a(n) for n = 0..999
Index entries for linear recurrences with constant coefficients, signature (10).

Cf. A000533, A011557, A057427, A061601, A070565, A109002, A155559, A178501.

Partial sums of A063945.

Array[10^#*Sign[#] &, 20, 0] (* Michael De Vlieger, Apr 21 2019 *)

a(n) = A011557(n)*A057427(n).
For n > 0, a(n) = A011557(n).
a(n) = 10*A178501(n).
a(n) = A000533(n) - 1.
A061601(a(n)) = A109002(n+1).
From Elmo R. Oliveira, Jul 21 2025: (Start)
G.f.: 10*x/(1-10*x).
E.g.f.: 2*exp(5*x)*sinh(5*x).
a(n) = 10*a(n-1) for n > 1. (End)

A198698 a(n) = 3*10^n - 1.

Original entry on oeis.org

2, 29, 299, 2999, 29999, 299999, 2999999, 29999999, 299999999, 2999999999, 29999999999, 299999999999, 2999999999999, 29999999999999, 299999999999999, 2999999999999999, 29999999999999999, 299999999999999999, 2999999999999999999, 29999999999999999999, 299999999999999999999

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002283, A109002.

Magma
```
[3*10^n-1: n in [0..30]];
```

a(n) = 10*a(n-1) + 9, a(0)=2.
a(n) = 11*a(n-1) - 10*a(n-2), n>1.
G.f.: (2+7*x)/((10*x-1)*(x-1)). - R. J. Mathar, Oct 30 2011
E.g.f.: exp(x)*(3*exp(9*x) - 1). - Elmo R. Oliveira, Jun 13 2025

A198699 a(n) = 7*10^n - 1.

Original entry on oeis.org

6, 69, 699, 6999, 69999, 699999, 6999999, 69999999, 699999999, 6999999999, 69999999999, 699999999999, 6999999999999, 69999999999999, 699999999999999, 6999999999999999, 69999999999999999, 699999999999999999, 6999999999999999999, 69999999999999999999, 699999999999999999999

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002283, A109002, A198972.

Magma
```
[7*10^n-1: n in [0..30]];
```

NestList[10#+9&,6,20] (* or *) LinearRecurrence[{11,-10},{6,69},20] (* Harvey P. Dale, Dec 29 2013 *)

a(n) = 10*a(n-1) + 9.
a(n) = 11*a(n-1) - 10*a(n-2), n>1.
G.f.: (6+3*x)/((10*x-1)*(x-1)). - R. J. Mathar, Oct 29 2011
From Elmo R. Oliveira, Jun 14 2025: (Start)
E.g.f.: exp(x)*(7*exp(9*x) - 1).
a(n) = 3*A198972(n). (End)

A198700 a(n) = 11*10^n - 1.

Original entry on oeis.org

10, 109, 1099, 10999, 109999, 1099999, 10999999, 109999999, 1099999999, 10999999999, 109999999999, 1099999999999, 10999999999999, 109999999999999, 1099999999999999, 10999999999999999, 109999999999999999, 1099999999999999999, 10999999999999999999, 109999999999999999999

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002283, A066007, A109002.

Cf. A096209 (primes).

Magma
```
[11*10^n-1: n in [0..30]];
```

(11 10^Range[0,20])-1 (* or  *) LinearRecurrence[{11,-10},{10,109},20] (* Harvey P. Dale, Nov 29 2020 *)

a(n) = 10*a(n-1) + 9.
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: (10-x)/((10*x-1)*(x-1)). - R. J. Mathar, Oct 29 2011
E.g.f.: exp(x)*(11*exp(9*x) - 1). - Elmo R. Oliveira, Aug 23 2024

A093948 Primes of the form 9*10^k - 1.

Original entry on oeis.org

89, 8999, 89999999, 89999999999999999999, 899999999999999999999999999999, 89999999999999999999999999999999999999, 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Offset: 1

Rick L. Shepherd, Apr 17 2004

nonn

Equivalently, primes of the form 8*10^k + 9*R_k, where R_k is the repunit (A002275) of length k.

Makoto Kamada, Prime numbers of the form 899...999.
Index entries for primes involving repunits.

Cf. A002275, A056725 (corresponding k).

Primes in A109002.

a(n) = 9*10^A056725(n) - 1 = A109002(A056725(n) + 1). - Elmo R. Oliveira, Jun 14 2025

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula

Extensions

A178500 a(n) = 10^n * signum(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A198698 a(n) = 3*10^n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

A198699 a(n) = 7*10^n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A198700 a(n) = 11*10^n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A093948 Primes of the form 9*10^k - 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula