This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A178769 #32 Sep 09 2024 20:03:40
%S A178769 2,7,57,557,5557,55557,555557,5555557,55555557,555555557,5555555557,
%T A178769 55555555557,555555555557,5555555555557,55555555555557,
%U A178769 555555555555557,5555555555555557,55555555555555557,555555555555555557,5555555555555555557,55555555555555555557,555555555555555555557
%N A178769 a(n) = (5*10^n + 13)/9.
%H A178769 Bruno Berselli, <a href="/A178769/b178769.txt">Table of n, a(n) for n = 0..1000</a>.
%H A178769 Bruno Berselli, <a href="http://www.base5forum.it/upload/57_46.gif">A property that includes the numbers of the form 5..57</a>.
%H A178769 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A178769 a(n)^(4*k+2) + 1 == 0 (mod 250) for n > 1, k >= 0.
%F A178769 G.f.: (2-15*x)/((1-x)*(1-10*x)).
%F A178769 a(n) - 11*a(n-1) + 10*a(n-2) = 0 (n > 1).
%F A178769 a(n) = a(n-1) + 5*10^(n-1) = 10*a(n-1) - 13 for n > 0.
%F A178769 a(n) = 1 + Sum_{i=0..n} A093143(i). - _Bruno Berselli_, Feb 16 2015
%F A178769 E.g.f.: exp(x)*(5*exp(9*x) + 13)/9. - _Elmo R. Oliveira_, Sep 09 2024
%t A178769 CoefficientList[Series[(2 - 15 x) / ((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%t A178769 LinearRecurrence[{11,-10},{2,7},20] (* _Harvey P. Dale_, Feb 28 2017 *)
%o A178769 (Magma) [(5*10^n+13)/9: n in [0..20]]; // _Vincenzo Librandi_, Jun 06 2013
%o A178769 (PARI) vector(20, n, n--; (5*10^n+13)/9) \\ _G. C. Greubel_, Jan 24 2019
%o A178769 (Sage) [(5*10^n+13)/9 for n in (0..20)] # _G. C. Greubel_, Jan 24 2019
%o A178769 (GAP) List([0..20], n -> (5*10^n+13)/9); # _G. C. Greubel_, Jan 24 2019
%Y A178769 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,..).
%Y A178769 Cf. A093143.
%K A178769 nonn,easy
%O A178769 0,1
%A A178769 _Bruno Berselli_, Jun 13 2010