The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A079898 a(1) = 1; a(n) = tau(n) - tau(n-1)* a(n-1) if n > 1. 1
 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; refs; listen; history; text; internal format)
 OFFSET 1,4 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 tau(n). In general the integral oscillator of s(n) can be defined similarly. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 MATHEMATICA 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] RecurrenceTable[{a[1]==1, a[n]==DivisorSigma[0, n]-DivisorSigma[0, n-1]a[n-1]}, a, {n, 30}] (* Harvey P. Dale, Sep 17 2018 *) CROSSREFS Sequence in context: A259885 A110578 A134045 * A173449 A270519 A212848 Adjacent sequences:  A079895 A079896 A079897 * A079899 A079900 A079901 KEYWORD sign AUTHOR Joseph L. Pe, Feb 20 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 1 07:40 EDT 2020. Contains 334759 sequences. (Running on oeis4.)