OFFSET
1,1
COMMENTS
For more details about this type of expansions, see A233582.
The cases with known periodic expansions, listed in A233592, all become periodic after just two leading terms. In contrast, the Blazys's expansion of sqrt(a(k)) for every member a(k) of this list remains aperiodic up to at least 1000 terms. It is therefore conjectured, though not proved, that these expansions are indeed aperiodic.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..200
Stanislav Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013.
Stanislav Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki.
EXAMPLE
Blazys's expansion of sqrt(7), A233587, is {2, 3, 30, 34, 111, ...}. Its first 1000 terms are all distinct. Hence, 7 is a term of this sequence.
CROSSREFS
KEYWORD
nonn
AUTHOR
Stanislav Sykora, Jan 06 2014
STATUS
approved