Search: id:A117581 Results 1-1 of 1 results found. %I A117581 %S A117581 2,9,81,4375,9801,123201,336141,11859211,11859211,177182721,1611308700, %T A117581 3463200000,63927525376,421138799640,1109496723126,1453579866025, %U A117581 20628591204481,31887350832897,31887350832897,119089041053697 %N 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. By a theorem of Stormer, the number of such integers is finite; moreover he provides an algorithm for finding the complete list. %C A117581 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. %D A117581 Lehmer, D. H., "On a Problem of Stormer", Illinois Journal of Mathematics, vol. 8, no 1, (1964), pp. 51-79 %H A117581 Wikipedia, Stormer's Theorem %Y A117581 Cf. A002071, A116486, A117582, A117583. Equals A002072(n) + 1. %Y A117581 Sequence in context: A135868 A147302 A112670 this_sequence A123570 A006040 A067309 %Y A117581 Adjacent sequences: A117578 A117579 A117580 this_sequence A117582 A117583 A117584 %K A117581 nonn %O A117581 1,1 %A A117581 Gene Ward Smith (genewardsmith(AT)gmail.com), Mar 29 2006 %E A117581 Entry edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 01 2006 %E A117581 Corrected and extended by Don Reble, Nov 21 2006 Search completed in 0.001 seconds