A086942 -id:A086942 - 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

A086943 Integers k such that R(k+7) = 3.

Original entry on oeis.org

23, 293, 2993, 29993, 299993, 2999993, 29999993, 299999993, 2999999993, 29999999993, 299999999993, 2999999999993, 29999999999993, 299999999999993, 2999999999999993, 29999999999999993, 299999999999999993, 2999999999999999993, 29999999999999999993, 299999999999999999993

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, A086942.

[3*10^n-7: n in [1..25] ]; // Vincenzo Librandi, Aug 22 2011

FromDigits/@Table[Join[{2},Table[9,{n}],{3}],{n,0,20}] (* Harvey P. Dale, Aug 21 2011 *)
Table[ 10*FromDigits[PadRight[{2},n,9]]+3,{n,20}] (* Harvey P. Dale, Aug 05 2025 *)

A086943(n):=3*10^n-7$
makelist(A086943(n),n,1,17); /* Martin Ettl, Nov 08 2012 */

a(n) = 3*10^n - 7.
R(a(n)) = A086942(n).
From Elmo R. Oliveira, Apr 30 2025: (Start)
G.f.: x*(40*x+23)/((x-1)*(10*x-1)).
E.g.f.: 4 - 7*exp(x) + 3*exp(10*x).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

A086940 a(n) = k where R(k+4) = 2.

Original entry on oeis.org

16, 196, 1996, 19996, 199996, 1999996, 19999996, 199999996, 1999999996, 19999999996, 199999999996, 1999999999996, 19999999999996, 199999999999996, 1999999999999996, 19999999999999996, 199999999999999996, 1999999999999999996, 19999999999999999996

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, A086942, A086945, A198971.

[2*(10^n-2): n in [1..20] ]; // Vincenzo Librandi, Aug 22 2011

Table[FromDigits[Join[PadRight[{1},n,9],{6}]],{n,20}] (* or *) 2 (10^Range[20] - 2) (* or *) LinearRecurrence[{11,-10},{16,196},20] (* Harvey P. Dale, Aug 11 2012 *)

a(n) = 2*(10^n - 2).
R(a(n)) = A086945(n).
a(n) = 11*a(n-1) - 10*a(n-2); a(1)=16, a(2)=196. - Harvey P. Dale, Aug 11 2012
From Elmo R. Oliveira, Apr 30 2025: (Start)
G.f.: 4*x*(5*x+4)/((x-1)*(10*x-1)).
E.g.f.: 2*(1 - 2*exp(x) + exp(10*x)).
a(n) = 4*A198971(n-1) = A086942(n)/2. (End)

cp's OEIS Frontend

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

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A086943 Integers k such that R(k+7) = 3.

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A086940 a(n) = k where R(k+4) = 2.

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