OFFSET
1,2
COMMENTS
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.
EXAMPLE
For n=1 there is 1 root, for n=2,...7 there are 2 roots, for n=8,...14 there are 6 roots, etc.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gordon Roesler, Jul 22 2012
EXTENSIONS
Terms after a(8) from T. D. Noe, Jul 30 2012
STATUS
approved