%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, <a href="http://en.wikipedia.org/wiki/Stormer%27s_theorem">
               Stormer's Theorem</a>
%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