A069508 a(1) = 6; a(n) = smallest palindromic number of the form k*a(n-1) + 1 with k > 1.

6, 55, 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}/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.: (440*x^3 - 434*x^2 - 11*x + 6)/((x - 1)*(10*x - 1)). (End)

Mathematica

CoefficientList[Series[(440 x^3 - 434 x^2 - 11 x + 6) / ((x - 1) (10 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 21 2016 *)

Prog

(Magma) I:=[6, 55, 111, 1111]; [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, A069506, A069507, A069509, A069510.

Sequence in context: A119218 A085066 A085067 * A079465 A061792 A066514

Adjacent sequences: A069505 A069506 A069507 * A069509 A069510 A069511

Keyword

nonn,base

Author

Amarnath Murthy, Mar 30 2002

Extensions

More terms from Patrick De Geest, Jun 11 2003

Status

approved