A069506 a(1) = 2; a(n) = smallest palindromic number of the form k*a(n-1) + 1 with k > 1.

2, 5, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11, -10).

Formula

a(n) = (10^(n-1)-1)/9 for n > 2.

From Chai Wah Wu, Jun 20 2016: (Start)

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

G.f.: (40*x^3 - 24*x^2 - 17*x + 2)/((x - 1)*(10*x - 1)). (End)

Mathematica

CoefficientList[Series[(40 x^3 - 24 x^2 - 17 x + 2) / ((x - 1) (10 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 21 2016 *)
LinearRecurrence[{11, -10}, {2, 5, 11, 111}, 20] (* Harvey P. Dale, Feb 01 2024 *)

Prog

(Magma) I:=[2, 5, 11, 111]; [n le 4 select I[n] else 11*Self(n-1)-10*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jun 21 2016

Crossrefs

Cf. A069505, A069507, A069508, A069509, A069510.

Sequence in context: A078790 A158999 A283300 * A239900 A123165 A098438

Adjacent sequences: A069503 A069504 A069505 * A069507 A069508 A069509

Keyword

nonn,base,easy

Author

Amarnath Murthy, Mar 30 2002

Extensions

More terms from Patrick De Geest, Jun 11 2003

Status

approved