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 A079883 a(1) = 1; a(n) = prime(n) - prime(n-1)* a(n-1) if n > 1. 0
 1, 1, 2, -3, 32, -339, 4424, -75189, 1428614, -32858093, 952884728, -29539426531, 1092958781688, -44811310049165, 1926886332114142, -90563657609364621, 4799873853296324972, -283192557344483173287, 17274745998013473570574, -1157407981866902729228387 (list; graph; refs; listen; history; text; internal format)
 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. For s(n) = prime(n), one has s'(n) = 1 - (p(n-1)/p(n)) s'(n-1) = [p(n) - p(n-1) s'(n-1)]/p(n). The numerator is the expression p(n) - p(n-1) s'(n-1), which motivates the definition of the above sequence a(n). a(n) is called the "integral oscillator" of prime(n). In general the integral oscillator of s(n) can be defined similarly. LINKS MATHEMATICA t = {1}; gt = 1; For[i = 2, i <= 24, i++, gt = Prime[i] - Prime[i - 1] gt; t = Append[t, gt]]; t ListPlot[t, PlotJoined -> True] CROSSREFS Cf. A069942. Sequence in context: A052830 A041895 A277481 * A066269 A083785 A046487 Adjacent sequences:  A079880 A079881 A079882 * A079884 A079885 A079886 KEYWORD sign AUTHOR Joseph L. Pe, Feb 20 2003 STATUS approved

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Last modified October 20 22:16 EDT 2018. Contains 316404 sequences. (Running on oeis4.)