login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..20.

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

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

License Agreements, Terms of Use, Privacy Policy. .

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