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 A067272 #36 Jun 14 2025 23:47:50
%S A067272 1,19,199,1999,19999,199999,1999999,19999999,199999999,1999999999,
%T A067272 19999999999,199999999999,1999999999999,19999999999999,
%U A067272 199999999999999,1999999999999999,19999999999999999,199999999999999999,1999999999999999999,19999999999999999999,199999999999999999999
%N A067272 a(n) = 2*10^(n-1) - 1.
%C A067272 Smaller of the smallest pair of successive n-digit numbers which have no digit in common: (1,2), (19,20), (199,200) etc. - _Amarnath Murthy_, Nov 10 2002
%C A067272 Original name: Numbers n such that the digits of T(n) = n*(n+1)/2, the n-th triangular number, begin with n.
%H A067272 Vincenzo Librandi, <a href="/A067272/b067272.txt">Table of n, a(n) for n = 1..200</a>
%H A067272 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A067272 a(n) = 2*10^(n-1) - 1. - _Benoit Cloitre_, Feb 28 2002
%F A067272 a(n) = 10*a(n-1) + 9. - _Vincenzo Librandi_, Nov 01 2011
%F A067272 G.f.: x*(1+8*x)/((1-x)*(1-10*x)). - _Vincenzo Librandi_, Aug 13 2014
%F A067272 From _Elmo R. Oliveira_, Jun 14 2025: (Start)
%F A067272 E.g.f.: (4 - 5*exp(x) + exp(10*x))/5.
%F A067272 a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
%e A067272 T(19) = 190 begins with 19. Hence 19 is a term of the sequence.
%t A067272 (*returns true if a begins with b, false o.w.*) f2[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[1]] == 1, r = True]]; r]; Do[If[f2[n(n + 1)/2, n], Print[n]], {n, 1, 10^6} ]
%t A067272 CoefficientList[Series[(1 + 8 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 13 2014 *)
%o A067272 (Magma) [2*10^(n-1)-1 : n in [1..20]]; // _Vincenzo Librandi_, Nov 01 2011
%o A067272 (PARI) a(n) = 2*10^(n-1)-1; \\ _Michel Marcus_, Jul 06 2024
%K A067272 nonn,easy
%O A067272 1,2
%A A067272 _Joseph L. Pe_, Feb 21 2002
%E A067272 a(7)-a(19) from _Vincenzo Librandi_, Nov 01 2011