A086940 -id:A086940 - cp's OEIS frontend

A198971 a(n) = 5*10^n - 1.

4, 49, 499, 4999, 49999, 499999, 4999999, 49999999, 499999999, 4999999999, 49999999999, 499999999999, 4999999999999, 49999999999999, 499999999999999, 4999999999999999, 49999999999999999, 499999999999999999, 4999999999999999999, 49999999999999999999, 499999999999999999999

Offset: 0

Vincenzo Librandi, Nov 02 2011

Also maximal value of GCD of 2 distinct (n+1)-digit numbers (compare with A126687). - Michel Marcus, Jun 24 2013
Also, a(n) is the largest obtained remainder when an (n+1)-digit number m is divided by any k with 1 <= k <= m. This remainder is obtained when 10^(n+1)-1 is divided by 5*10^n, example: 999 = 500 * 1 + 499, and a(2) = 499. - Bernard Schott, Nov 23 2021
Also numbers k whose digital reversal equals 2*(k - 2). - Stefano Spezia, Sep 15 2024

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

Cf. A002283, A086940, A086942, A099150, A126687.

Magma
```
[5*10^n-1 : n in [0..20]];
```

CoefficientList[Series[(4 + 5*x)/(1 - 11*x + 10*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)
LinearRecurrence[{11,-10},{4,49},20] (* Harvey P. Dale, Dec 30 2018 *)

a(n)=5*10^n-1 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 10*a(n-1) + 9.
a(n) = 11*a(n-1) - 10*a(n-2), n>1.
G.f.: (4 + 5*x)/(1 - 11*x + 10*x^2). - Vincenzo Librandi, Jan 03 2013
E.g.f.: exp(x)*(5*exp(9*x) - 1). - Stefano Spezia, Nov 17 2022
a(n) = A086942(n+1)/8 = A086940(n+1)/4 = A099150(n+1)/2. - Elmo R. Oliveira, May 02 2025

A086942 Integers k such that R(k+8) = 4.

Original entry on oeis.org

32, 392, 3992, 39992, 399992, 3999992, 39999992, 399999992, 3999999992, 39999999992, 399999999992, 3999999999992, 39999999999992, 399999999999992, 3999999999999992, 39999999999999992, 399999999999999992, 3999999999999999992, 39999999999999999992

Offset: 1

Ray Chandler, Jul 24 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A086940, A086943, A099150, A198971.

[4*10^n-8: n in [1..25]]; // Vincenzo Librandi, Aug 22 2011

4*10^Range[20] - 8 (* Paolo Xausa, Sep 21 2024 *)

a(n) = 4*10^n - 8.
R(a(n)) = A086943(n).
G.f.: 8*x*(5*x+4)/((10*x-1)*(x-1)).
a(n) = 8*A198971(n-1).
From Elmo R. Oliveira, May 01 2025: (Start)
E.g.f.: 4*(1 - 2*exp(x) + exp(10*x)).
a(n) = 4*A099150(n) = 2*A086940(n).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

A086945 a(n) = 7*10^n - 9.

Original entry on oeis.org

61, 691, 6991, 69991, 699991, 6999991, 69999991, 699999991, 6999999991, 69999999991, 699999999991, 6999999999991, 69999999999991, 699999999999991, 6999999999999991, 69999999999999991, 699999999999999991, 6999999999999999991, 69999999999999999991

Offset: 1

Ray Chandler, Jul 24 2003

a(n) = k where R(k+9) = 7.

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A086940.

[7*10^n-9: n in [1..25] ]; // Vincenzo Librandi, Aug 22 2011

Table[10 FromDigits[PadRight[{6},n,9]]+1,{n,20}] (* Harvey P. Dale, Aug 14 2021 *)

R(a(n)) = A086940(n).
From Elmo R. Oliveira, Apr 30 2025: (Start)
G.f.: x*(20*x+61)/((x-1)*(10*x-1)).
E.g.f.: 2 - 9*exp(x) + 7*exp(10*x).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

cp's OEIS Frontend

A198971 a(n) = 5*10^n - 1.

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A086942 Integers k such that R(k+8) = 4.

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A086945 a(n) = 7*10^n - 9.

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