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Search: id:A117581
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| A117581 |
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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. By a theorem of Stormer, the number of such integers is finite; moreover he provides an algorithm for finding the complete list. |
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2
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| 2, 9, 81, 4375, 9801, 123201, 336141, 11859211, 11859211, 177182721, 1611308700, 3463200000, 63927525376, 421138799640, 1109496723126, 1453579866025, 20628591204481, 31887350832897, 31887350832897, 119089041053697
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Stormer 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.
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REFERENCES
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Lehmer, D. H., "On a Problem of Stormer", Illinois Journal of Mathematics, vol. 8, no 1, (1964), pp. 51-79
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LINKS
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Wikipedia, Stormer's Theorem
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CROSSREFS
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Cf. A002071, A116486, A117582, A117583. Equals A002072(n) + 1.
Sequence in context: A109519 A135868 A112670 this_sequence A123570 A006040 A067309
Adjacent sequences: A117578 A117579 A117580 this_sequence A117582 A117583 A117584
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KEYWORD
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nonn
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AUTHOR
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Gene Ward Smith (genewardsmith(AT)gmail.com), Mar 29 2006
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EXTENSIONS
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Entry edited by njas, Apr 01 2006
Corrected and extended by Don Reble, Nov 21 2006
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