This site is supported by donations to The OEIS Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117581 For each successive prime p, the largest integer n such that both n and n-1 factor into primes less than or equal to p. 6
2, 9, 81, 4375, 9801, 123201, 336141, 11859211, 11859211, 177182721, 1611308700, 3463200000, 63927525376, 421138799640, 1109496723126, 1453579866025, 20628591204481, 31887350832897, 31887350832897, 119089041053697 (list; graph; refs; listen; history; text; internal format)



By a theorem of Størmer, the number of such integers is finite; moreover he provides an algorithm for finding the complete list.

Størmer came to this problem from music theory. Another way to formulate the statement of the theorem is that for any prime p, there are only a finite number of superparticular ratios R = n/(n-1) such that R factors into primes less than or equal to p. The numerator of the smallest such R for the i-th prime is the i-th element of the above sequence. For instance, 81/80, the syntonic comma, is the smallest 5-limit superparticular "comma", i.e., small ratio greater than one.


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

D. H. Lehmer, On a problem of Størmer, Ill. J. Math., 8 (1964), 57-79.

Wikipedia, Størmer's theorem


Cf. A002071, A116486, A117582, A117583. Equals A002072(n) + 1.

Sequence in context: A147302 A301861 A112670 * A110567 A123570 A006040

Adjacent sequences:  A117578 A117579 A117580 * A117582 A117583 A117584




Gene Ward Smith, Mar 29 2006


Entry edited by N. J. A. Sloane, Apr 01 2006

Corrected and extended by Don Reble, Nov 21 2006



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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 14:49 EDT 2019. Contains 323532 sequences. (Running on oeis4.)