This has to be due to the Pisotudinousness of GoldenRatio, and the +-1 slope of Sin at multiples of Pi. --Dan On Jul 13, 2014, at 10:33 PM, Bill Gosper <billgosper@gmail.com> wrote:

On Sun, Jul 13, 2014 at 8:57 PM, Bill Gosper <billgosper@gmail.com> wrote:

...

In[360]:= Table[GoldenRatio^n*Sin[π*GoldenRatio^n] // N[N[#, 99]] &, {n, 69, 105}]

Out[360]= {3.14159, 3.14159, -3.14159, -3.14159, -3.14159, 3.14159, 3.14159, 3.14159, -3.14159, -3.14159, -3.14159, 3.14159, 3.14159, 3.14159, -3.14159, -3.14159, -3.14159, 3.14159, 3.14159, 3.14159, -3.14159, -3.14159, -3.14159, 3.14159, 3.14159, 3.14159, -3.14159, -3.14159, -3.14159, 3.14159, 3.14159, 3.14159, -3.14159, -3.14159, -3.14159, 3.14159, 3.14159} --rwg

Whereas In[362]:=Table[ (Sqrt[2] + Sqrt[3])^n*Sin[π*(Sqrt[2] + Sqrt[3])^n]/π // N[N[#, 99]] &, {n, 69, 105}]

Out[362]= {6.81476*10^33, -1., 6.77788*10^34, -1., -4.89061*10^35, -1., -2.09519*10^36, -1., -4.56286*10^37, -1., -4.59961*10^38, -1., -3.15805*10^39, -1., 5.68896*10^40, -1., 2.91069*10^41, -1., -2.724*10^42, -1., -4.32617*10^43, -1., -4.06476*10^44, -1., 4.21738*10^44, -1., 6.08704*10^46, -1., 5.32596*10^47, -1., 1.94754*10^48, -1., 5.52776*10^49, -1., -5.72711*10^50, -1., -5.86847*10^51} --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun