%I #41 Apr 21 2023 13:00:52

%S 1,1,1,1,2,1,2,1,5,1,4,1,2,3,1,3,2,4,7,1,5,12,1,3,4,7,7,1,5,4,5,2,15,

%T 1,6,1,2,5,7,13,1,5,4,13,1,4,3,23,1,4,2,14,1,4,2,4,1,4,2,4,1,53,1,6,

%U 29,1,3,20,1,3,3,1,3,3,1,14,24,1,6,15,1,3,9,1,3,3,4,29,1,5,24,14,16,1,5,5,1,3,13,1,3,3,16

%N Define a sequence of rationals by S(1)=1; for n>=1, write S(1),...,S(n) as XY^k, Y nonempty, where the fractional exponent k is maximized, and set S(n+1)=k; sequence gives denominators of S(1), S(2), ...

%C k is the "fractional curling number" of S(1),...,S(n). The infinite sequence S(1), S(2), ... is a fractional analog of Gijswijt's sequence A090822.

%C For the first 1000 terms, 1 <= S(n) <= 2. Is this always true?

%C See A224762 for definition and Maple program.

%H Allan Wilks, <a href="/A224763/b224763.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from N. J. A. Sloane)

%H Allan Wilks, <a href="/A224762/a224762.txt">Table of n, S(n) for n = 1..10000</a> [The first 1000 terms were computed by _N. J. A. Sloane_]

%e The sequence S(1), S(2), ... begins 1, 1, 2, 1, 3/2, 1, 3/2, 2, 6/5, 1, 5/4, 1, 3/2, 4/3, 1, 4/3, 3/2, 5/4, 8/7, 1, 6/5, 13/12, 1, 4/3, 5/4, 8/7, 9/7, 1, 6/5, 5/4, 6/5, 3/2, 16/15, 1, 7/6, 1, 3/2, 6/5, 8/7, 14/13, 1, 6/5, 5/4, 16/13, 1, 5/4, 4/3, 24/23, 1, 5/4, 3/2, 15/14, 1, 5/4, 3/2, 7/4, ...

%p See A224762.

%Y Cf. A224762 (numerators), A090822.

%K nonn,frac

%O 1,5

%A Conference dinner party, Workshop on Challenges in Combinatorics on Words, Fields Institute, Toronto, Apr 22 2013, entered by _N. J. A. Sloane_