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 A093700 #24 Sep 10 2023 01:50:39
%S A093700 0,1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,13,13,14,15,16,16,17,18,19,19,20,
%T A093700 21,22,22,23,24,25,26,26,27,28,29,29,30,31,32,32,33,34,35,35,36,37,38,
%U A093700 39,39,40,41,42,43,44,45,45,46,47,48,48,49,50,51,52,52,53,54,55,55,56,57
%N A093700 Number of 9's immediately following the decimal point in the expansion of (3+sqrt(8))^n.
%C A093700 Number of 0's immediately following the decimal point in the expansion of (3-sqrt(8))^n.
%H A093700 Henri Cohen, Fernando Rodriguez Villegas, and Don Zagier, <a href="https://www.emis.de/journals/EM/expmath/volumes/9/9.html">Convergence Acceleration of Alternating Series</a>, Experiment. Math. Volume 9, Issue 1 (2000), 3-12, Project Euclid - Cornell Univ (see Proposition 1).
%H A093700 Robbert Fokkink, <a href="https://arxiv.org/abs/2309.01644">The Pell Tower and Ostronometry</a>, arXiv:2309.01644 [math.CO], 2023.
%H A093700 Math Forum, <a href="http://mathforum.org/library/drmath/view/55927.html">Triangular Numbers That are Perfect Squares</a>
%H A093700 Math Pages, <a href="http://www.mathpages.com/home/kmath305/kmath305.htm">On m = sqrt(sqrt(n) + sqrt(kn+1))</a> [Wrong link]
%H A093700 Robert Simms, <a href="https://web.archive.org/web/20080829235933/http://www.math.clemson.edu/~simms/neat/math/pyth/npyth.html">Using counting numbers to generate Pythagorean triples</a>
%F A093700 Roughly, floor(3*n/4)
%e A093700 Let n=10, (3+sqrt(8))^10= 45239073.9999999778... (the fractional part starts with seven 9's), so the 10th element in this sequence is 7.
%e A093700 The 132nd element is 100. The 1000th element is 765. The 1307th element is 1000.
%e A093700 The arrangement of repeating elements are like A074184 (Index of the smallest power of n >= n!) and A076539 (Numerators a(n) of fractions slowly converging to pi) and A080686 (Number of 19-smooth numbers <= n).
%t A093700 For[n = 1, n < 999, n++, Block[{$MaxExtraPrecision = 50*n}, Print[ -Floor[Log[10, 1 - N[FractionalPart[(3 + 2Sqrt[2])^n], n]]] - 1]]]
%t A093700 f[n_] := Block[{}, -MantissaExponent[(3 - Sqrt[8])^n][[2]]]; Table[ f[n], {n, 75}] (* _Robert G. Wilson v_, Apr 10 2004 *)
%Y A093700 Cf. A003499, A050608, A080686, A076539, A074184.
%K A093700 nonn,base
%O A093700 1,3
%A A093700 _Marvin Ray Burns_, Apr 10 2004