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, 5555555555555555551, 55555555555555555551, 555555555555555555551

Offset: 1

Author

Vincenzo Librandi, Feb 25 2010

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

[(5*10^n-41)/9: n in [1..20]]; // 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 *)

Formula

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

From Vincenzo Librandi, Jul 05 2012: (Start)

G.f.: x*(1+40*x)/((1-x)*(1-10*x)).

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

E.g.f.: 4 + exp(x)*(5*exp(9*x) - 41)/9. - Elmo R. Oliveira, Sep 09 2024