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

0,1

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).

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

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 *)

Prog

(Magma) [(5*10^n+13)/9: n in [0..20]]; // Vincenzo Librandi, Jun 06 2013
(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
(GAP) List([0..20], n -> (5*10^n+13)/9); # G. C. Greubel, Jan 24 2019

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.

Sequence in context: A034935 A337833 A294948 * A121079 A270395 A105183

Adjacent sequences: A178766 A178767 A178768 * A178770 A178771 A178772

Keyword

nonn,easy

Author

Bruno Berselli, Jun 13 2010

Status

approved