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.
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
LINKS
Lucas A. Brown, stormer.py.
D. H. Lehmer, On a problem of Størmer, Ill. J. Math., 8 (1964), 57-79.
Wikipedia, Størmer's theorem.
CROSSREFS
KEYWORD
nonn,hard
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