A085952 First n-digit number that occurs in the sequence A085951.

1, 91, 901, 9001, 90001, 900001, 9000001, 90000001, 900000001, 9000000001, 90000000001, 900000000001, 9000000000001, 90000000000001, 900000000000001, 9000000000000001, 90000000000000001, 900000000000000001, 9000000000000000001, 90000000000000000001, 900000000000000000001

Offset: 0

Author

Amarnath Murthy and Jason Earls, Jul 15 2003

Keywords

• nonn
• easy
• base

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A085951.

Programs

Magma

[1] cat [9*10^n+1: n in [1..30]]; // Vincenzo Librandi, Nov 09 2011

Mathematica

Join[{1},Table[9*10^n+1,{n,30}]] (* or *) LinearRecurrence[{11,-10},{1,91,901},30] (* Harvey P. Dale, Dec 19 2022 *)

Formula

For n > 0, a(n) = 9*10^n + 1. - David Wasserman, Feb 15 2005

From Elmo R. Oliveira, Jun 12 2025: (Start)

G.f.: (1 + 80*x - 90*x^2)/((10*x-1)*(x-1)).

E.g.f.: exp(x)*(1 + 9*exp(9*x)) - 9.

a(n) = 11*a(n-1) - 10*a(n-2) for n >= 3. (End)

Extensions

Corrected and extended by David Wasserman, Feb 15 2005