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%I #26 Oct 17 2022 01:58:42
%S 2,9,81,4375,9801,123201,336141,11859211,11859211,177182721,
%T 1611308700,3463200000,63927525376,421138799640,1109496723126,
%U 1453579866025,20628591204481,31887350832897,31887350832897,119089041053697
%N 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.
%C By a theorem of Størmer, the number of such integers is finite; moreover he provides an algorithm for finding the complete list.
%C 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.
%C An effective abc conjecture (c < rad(abc)^2) would imply that a(21) = 2286831727304145 and a(22) = ... = a(26) = 9591468737351909376 and a(27) = ... = a(32) = 19316158377073923834001 and a(33) = 124225935845233319439174. - _Lucas A. Brown_, Oct 16 2022
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/stormer.py">stormer.py</a>.
%H D. H. Lehmer, <a href="http://projecteuclid.org/euclid.ijm/1256067456">On a problem of Størmer</a>, Ill. J. Math., 8 (1964), 57-79.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Stormer%27s_theorem">Størmer's theorem</a>.
%Y Cf. A002071, A116486, A117582, A117583. Equals A002072(n) + 1.
%K nonn,hard
%O 1,1
%A _Gene Ward Smith_, Mar 29 2006
%E Entry edited by _N. J. A. Sloane_, Apr 01 2006
%E Corrected and extended by _Don Reble_, Nov 21 2006
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