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 A213082 #19 Jul 30 2012 22:00:07
%S A213082 1,2,8,15,21,27,33,40,46,52,59,65,71,77,84,90,96,103,109,115,121,128,
%T A213082 134,140,147,153,159,165,172,178,184,191,197,203,209,216,222,228,235,
%U A213082 241,247,253,260,266,272,279,285,291,297,304,310,316,323,329,335
%N A213082 Values of n for which the number of roots of the function sin(x)/x - 1/n increases.
%C A213082 Maxima of sin(x)/x correspond to odd solutions of x(m)=tan(x(m)). At maxima, sin(x(m))/x(m)=sin(tan(x(m)))/tan(x(m)). Number of roots of f(x)=sin(x)/x - 1/n increases when n = int(x(m)/sin(x(m))+1.
%e A213082 For n=1 there is 1 root, for n=2,...7 there are 2 roots, for n=8,...14 there are 6 roots, etc.
%t A213082 t = Table[x*Cos[x] - Sin[x], {x, 400}]; t2 = {1, 2}; Do[If[t[[n]] > 0 && t[[n + 1]] < 0, AppendTo[t2, n + 1]], {n, Length[t] - 1}]; t2 (* _T. D. Noe_, Jul 30 2012 *)
%K A213082 nonn
%O A213082 1,2
%A A213082 _Gordon Roesler_, Jul 22 2012
%E A213082 Terms after a(8) from _T. D. Noe_, Jul 30 2012