%I #3 Feb 11 2014 19:05:41
%S 1,0,2,-2,8,-30,66,-392,1574,-9440,37770,-377696,1510796,-18129546,
%T 108777284,-870218264,6961746128,-111387938042,668327628270,
%U -12029897308852,96239178470828,-1154870141649926,11548701416499282,-254071431162984196,2032571449303873588
%N a(1) = 1; a(n) = phi(n) - phi(n-1)* a(n-1) if n > 1.
%C 1. Let s(n) be a sequence such that lim s(n)/s(n+1) = K different from -1. The "oscillator sequence" (or simply "oscillator") of s(n) is the sequence s'(n) defined by the rules: s'(1) = 1; s'(n) = 1 - (s(n-1)/s(n)) s'(n-1). 2. It is an open problem whether the oscillator (prime)' converges to 1/2 or diverges. 3. s'(n) = 1 - (s(n-1)/s(n)) s'(n-1) = [s(n) - s(n-1) s'(n-1)]/s(n). The numerator is the expression s(n) - s(n-1) s'(n-1), which motivates the definition of the above sequence a(n). a(n) is called the "integral oscillator" of phi(n). In general the integral oscillator of s(n) can be defined similarly.
%t t = {1}; gt = 1; For[i = 2, i <= 30, i++, gt = EulerPhi[i] - EulerPhi[i - 1] gt; t = Append[t, gt]]; t ListPlot[t, PlotJoined -> True]
%K sign
%O 1,3
%A _Joseph L. Pe_, Feb 20 2003