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A233593 Natural numbers n such that the continued fraction expansion sqrt(n) = c(1)+c(1)/(c(2)+c(2)/(c(3)+c(3)/....)) is aperiodic. 3
7, 13, 14, 19, 21, 22, 23, 28, 29, 31, 32, 33, 34, 41, 43, 46, 47, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 85, 86, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 103, 106, 107 (list; graph; refs; listen; history; text; internal format)
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 a-periodic 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

S. Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001

S. Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki

EXAMPLE

Blazys' expansion of sqrt(7), A233587, is {2,3,30,34,111,...}. Its first 1000 terms are all different. Hence, 7 is a member of this list.

CROSSREFS

Cf. A233592.

Cf. Blazys's expansions: A233582, A233584, A233585, A233586, A233587.

Sequence in context: A194408 A057930 A332480 * A013651 A050931 A072864

Adjacent sequences:  A233590 A233591 A233592 * A233594 A233595 A233596

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Jan 06 2014

STATUS

approved

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Last modified May 26 08:39 EDT 2020. Contains 334620 sequences. (Running on oeis4.)