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A079895
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a(1) = 1; a(n) = phi(n) - phi(n-1)* a(n-1) if n > 1.
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1, 0, 2, -2, 8, -30, 66, -392, 1574, -9440, 37770, -377696, 1510796, -18129546, 108777284, -870218264, 6961746128, -111387938042, 668327628270, -12029897308852, 96239178470828, -1154870141649926, 11548701416499282, -254071431162984196, 2032571449303873588
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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.
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MATHEMATICA
| 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]
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CROSSREFS
| Sequence in context: A054093 A098557 A003616 * A053047 A076143 A057132
Adjacent sequences: A079892 A079893 A079894 * A079896 A079897 A079898
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KEYWORD
| sign
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 20 2003
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