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Search: id:A079898
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| A079898 |
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a(1) = 1; a(n) = tau(n) - tau(n-1)* a(n-1) if n > 1. |
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+0
1
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| 1, 1, 0, 3, -7, 18, -70, 144, -573, 1723, -6890, 13786, -82714, 165432, -661724, 2646901, -13234503, 26469012, -158814070, 317628146, -1905768872, 7623075492, -30492301966, 60984603940, -487876831517, 1463630494555, -5854521978216, 23418087912870, -140508527477218
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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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 tau(n). In general the integral oscillator of s(n) can be defined similarly.
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MATHEMATICA
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t = {1}; gt = 1; For[i = 2, i <= 30, i++, gt = DivisorSigma[0, i] - DivisorSigma[0, i - 1] gt; t = Append[t, gt]]; t ListPlot[t, PlotJoined -> True]
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CROSSREFS
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Adjacent sequences: A079895 A079896 A079897 this_sequence A079899 A079900 A079901
Sequence in context: A062416 A110578 A134045 this_sequence A088629 A075609 A083439
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KEYWORD
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sign
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 20 2003
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