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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054540 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the six simple ratios of musical harmony: 6/5, 5/4, 4/3, 3/2, 8/5 and 5/3. 20
1, 2, 3, 5, 7, 12, 19, 31, 34, 53, 118, 171, 289, 323, 441, 612, 730, 1171, 1783, 2513, 4296, 12276, 16572, 20868, 25164, 46032, 48545, 52841, 73709, 78005, 151714, 229719, 537443, 714321, 792326, 944040, 1022045, 1251764, 3755292, 3985011 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence was found by a computer search of all of the equal divisions of the octave from 1 to over 3985011. There seems to be a hidden aspect or mystery here: what is it about the more and more harmonious equal temperaments that causes them to express themselves collectively as a perfect, self-accumulating recurrent sequence?

LINKS

Table of n, a(n) for n=0..39.

FORMULA

Stochastic recurrence rule - the next term equals the current term plus one or more previous terms: a(n+1) = a(n) + a(n-x)... + a(n-y)... + a(n-z), etc.

EXAMPLE

34 = 31 + the earlier term 3. Again, 118 = 53 + the earlier terms 34 and 31.

CROSSREFS

Cf. A001149, A018065, A001856, A002858, A007335, A060525-A060527.

Sequence in context: A143642 A192685 A060986 * A216231 A117537 A137713

Adjacent sequences:  A054537 A054538 A054539 * A054541 A054542 A054543

KEYWORD

nonn

AUTHOR

Mark William Rankin (MarkRankin95511(AT)Yahoo.com), Apr 09 2000; Dec 17 2000

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 December 5 07:11 EST 2016. Contains 278761 sequences.