

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), ...


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
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OFFSET

1,5


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.


LINKS

Allan Wilks, Table of n, a(n) for n = 1..10000 (terms 1..1000 from by 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]


EXAMPLE

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, ...


MAPLE

See A224762.


CROSSREFS

Cf. A224762 (numerators), A090822.
Sequence in context: A260612 A159829 A343593 * A128515 A332489 A119569
Adjacent sequences: A224760 A224761 A224762 * A224764 A224765 A224766


KEYWORD

nonn,frac


AUTHOR

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


STATUS

approved



