A178769 a(n) = (5*10^n + 13)/9.

2, 7, 57, 557, 5557, 55557, 555557, 5555557, 55555557, 555555557, 5555555557, 55555555557, 555555555557, 5555555555557, 55555555555557, 555555555555557, 5555555555555557, 55555555555555557, 555555555555555557, 5555555555555555557, 55555555555555555557, 555555555555555555557

Offset: 0

Author

Bruno Berselli, Jun 13 2010

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000.
• Bruno Berselli, A property that includes the numbers of the form 5..57.
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A165246 (..17, 117, 1117,..), A173193 (..27, 227, 2227,..), A173766 (..37, 337, 3337,..), A173772 (..47, 447, 4447,..), A067275 (..67, 667, 6667,..), A002281 (..77, 777, 7777,..), A173812 (..87, 887, 8887,..), A173833 (..97, 997, 9997,..).

Cf. A093143.

Programs

GAP

List([0..20], n -> (5*10^n+13)/9); # G. C. Greubel, Jan 24 2019

Magma

[(5*10^n+13)/9: n in [0..20]]; // Vincenzo Librandi, Jun 06 2013

Mathematica

CoefficientList[Series[(2 - 15 x) / ((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{11,-10},{2,7},20] (* Harvey P. Dale, Feb 28 2017 *)

PARI

vector(20, n, n--; (5*10^n+13)/9) \\ G. C. Greubel, Jan 24 2019

Sage

[(5*10^n+13)/9 for n in (0..20)] # G. C. Greubel, Jan 24 2019

Formula

a(n)^(4*k+2) + 1 == 0 (mod 250) for n > 1, k >= 0.

G.f.: (2-15*x)/((1-x)*(1-10*x)).

a(n) - 11*a(n-1) + 10*a(n-2) = 0 (n > 1).

a(n) = a(n-1) + 5*10^(n-1) = 10*a(n-1) - 13 for n > 0.

a(n) = 1 + Sum_{i=0..n} A093143(i). - Bruno Berselli, Feb 16 2015

E.g.f.: exp(x)*(5*exp(9*x) + 13)/9. - Elmo R. Oliveira, Sep 09 2024