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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)
OFFSET

1,1

COMMENTS

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.

LINKS

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Gene Ward Smith, Mar 29 2006

EXTENSIONS

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

Corrected and extended by Don Reble, Nov 21 2006

STATUS

approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)