A173804 a(n) = (5*10^n - 41)/9 for n > 0.

1, 51, 551, 5551, 55551, 555551, 5555551, 55555551, 555555551, 5555555551, 55555555551, 555555555551, 5555555555551, 55555555555551, 555555555555551, 5555555555555551, 55555555555555551, 555555555555555551

Offset

1,2

Comments

Primes up to n=100 are 555555555551 and 5555555555551; the next prime term has 609 digits (see A056684).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

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

Formula

a(n) = 10*a(n-1) + 41 with a(0)=-4.

G.f.: x*(1+40*x)/((1-x)*(1-10*x)). - Vincenzo Librandi, Jul 05 2012

a(n) = 11*a(n-1) - 10*a(n-2). - Vincenzo Librandi, Jul 05 2012

Mathematica

CoefficientList[Series[(1+40*x)/((1-x)*(1-10*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 05 2012 *)
Table[FromDigits[PadLeft[{1}, n, 5]], {n, 20}] (* or *) LinearRecurrence[ {11, -10}, {1, 51}, 20](* Harvey P. Dale, Dec 04 2021 *)

Prog

(Magma)[(5*10^n-41)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012

Crossrefs

Cf. A056684 (numbers n such that (5*10^(n+1)-41)/9 is prime). - Klaus Brockhaus, Feb 28 2010

Sequence in context: A142994 A251932 A319542 * A166820 A269438 A269622

Adjacent sequences: A173801 A173802 A173803 * A173805 A173806 A173807

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 25 2010

Status

approved