A086947 Numbers k such that R(k+9) = 3.

21, 291, 2991, 29991, 299991, 2999991, 29999991, 299999991, 2999999991, 29999999991, 299999999991, 2999999999991, 29999999999991, 299999999999991, 2999999999999991, 29999999999999991, 299999999999999991, 2999999999999999991, 29999999999999999991, 299999999999999999991

Offset: 1

Author

Ray Chandler, Jul 24 2003

Keywords

• nonn
• base
• easy

Comments

If k is in this sequence then Reverse(k) = (2/3)*k - 2. Also A101703 is the sequence of all numbers k such that Reverse(k) = (2/3)*k - 2. So this sequence is a subsequence of A101703. - Farideh Firoozbakht, Dec 30 2004

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, A085331, A086948, A101700, A101703, A173833.

Programs

Magma

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

Mathematica

Table[3*(10^n-3), {n, 17}]
Table[FromDigits[PadRight[{3},n,0]],{n,2,20}]-9 (* Harvey P. Dale, Nov 27 2012 *)

Formula

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

R(a(n)) = A086948(n).

From Chai Wah Wu, Aug 01 2020: (Start)

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

G.f.: x*(60*x + 21)/((x - 1)*(10*x - 1)). (End)

From Elmo R. Oliveira, May 01 2025: (Start)

E.g.f.: 3*(2 - 3*exp(x) + exp(10*x)).

a(n) = 3*A173833(n). (End)