A224763 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), ...

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, 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, 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

Offset: 1

Author

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

Keywords

• nonn
• frac

Comments

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.

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

See A224762 for definition and Maple program.

Examples

			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, ...
		

Links

• Allan Wilks, Table of n, a(n) for n = 1..10000 (terms 1..1000 from N. J. A. Sloane)
• Allan Wilks, Table of n, S(n) for n = 1..10000 [The first 1000 terms were computed by _N. J. A. Sloane_]

Crossrefs

Cf. A224762 (numerators), A090822.

Programs

Maple

See A224762.