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 A068092 #33 Oct 17 2022 10:47:41
%S A068092 1,4,14,45,141,447,1414,4472,14142,44721,141421,447214,1414214,
%T A068092 4472136,14142136,44721360,141421356,447213595,1414213562,4472135955,
%U A068092 14142135624,44721359550,141421356237,447213595500,1414213562373,4472135955000,14142135623731
%N A068092 Index of smallest triangular number with n digits.
%C A068092 Look at the interleaving of the decimal expansion of the square roots of 2 and 20.
%H A068092 Vincenzo Librandi, <a href="/A068092/b068092.txt">Table of n, a(n) for n = 1..300</a>
%F A068092 a(n) = b where b = floor(sqrt(2*10^(n-1))) and if b(b+1)/2 < 10^(n-1), then b = b+1. [corrected by _Ray Chandler_, Oct 04 2011]
%F A068092 a(n) = round((2*10^(n-1))^(1/2)). - _Vladeta Jovovic_, Mar 08 2004
%F A068092 a(n) = A002024(10^(n-1)). - _Michel Marcus_, Jan 27 2022
%e A068092 a(4) = 45 as the 45th triangular number is 45*46/2 = 1035 while the 44th is 990.
%t A068092 f[n_] := Block[{a = Floor[Sqrt[2*10^n]]}, If[a(a + 1)/2 < 10^n, a++ ]; Return[a]]; Table[ f[n], {n, 0, 30} ]
%o A068092 (PARI) a(n) = round(sqrt(2*10^(n-1))) \\ _Charles R Greathouse IV_, Oct 04 2011
%o A068092 (Magma) [Round(Sqrt(2*10^(n-1))) : n in [1..30]]; // _Vincenzo Librandi_, Oct 05 2011
%o A068092 (Python)
%o A068092 from math import isqrt
%o A068092 def A068092(n): return isqrt(10**(n-1)<<3)+1>>1 # _Chai Wah Wu_, Oct 17 2022
%Y A068092 Cf. A002024, A002193, A010476.
%Y A068092 Cf. A068093, A068094, A095863, A095864, A095865, A095866.
%K A068092 base,easy,nonn
%O A068092 1,2
%A A068092 _Amarnath Murthy_, Feb 19 2002
%E A068092 Edited and extended by _Robert G. Wilson v_, Feb 21 2002