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

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

Offset: 1

Author

Ray Chandler, Jul 24 2003

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. A004086, A086942, A086945, A198971.

Programs

Magma

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

Mathematica

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 *)

Formula

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)