Good grief: In[239]:= Position[Sign[Convergents[2*Zeta[3], 777]/Convergents[Zeta[3], 777] - 2], 0] Out[239]= {{1}, {2}, {3}, {4}, {678}, {679}, {720}, {722}, {723}, {724}, {725}, {727}} vs In[240]:= Position[Sign[Convergents[2*Zeta[5], 77]/Convergents[Zeta[5], 77] - 2], 0] Out[240]= {{1}, {18}, {19}, {21}, {22}, {23}, {25}, {31}, {39}} --rwg FromHans Havermann: In preparation for next month's tau-day I've been playing with the continued fraction thereof. Consider the sign of nth convergent of 2*pi divided by the nth convergent of pi, minus 2. The first sixty are: 0, 1, -1, 1, -1, 1, -1, 0, 1, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 1, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, -1, 1, -1, 1, -1. I wasn't particularly surprised that stretches of non-zeros alternated sign. What impressed me was that the alternation continued *in step* after arbitrary-length stretches of zeros. _______________________________________________