A079895 a(1) = 1; a(n) = phi(n) - phi(n-1)* a(n-1) if n > 1.

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

Offset

1,3

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.

Links

Table of n, a(n) for n=1..25.

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]

Crossrefs

Sequence in context: A287496 A003616 A276657 * A351512 A053047 A076143

Adjacent sequences: A079892 A079893 A079894 * A079896 A079897 A079898

Keyword

sign

Author

Joseph L. Pe, Feb 20 2003

Status

approved