A233592 - OEIS

A233592

Positive integers k such that the continued fraction expansion sqrt(k) = c(1) + c(1)/(c(2) + c(2)/(c(3) + c(3)/...)) is periodic.

2, 3, 5, 6, 8, 10, 11, 12, 15, 17, 18, 20, 24, 26, 27, 30, 35, 37, 38, 39, 40, 42, 44, 45, 48, 50, 51, 56, 63, 65, 66, 68, 72, 80, 82, 83, 84, 87, 90, 99, 101, 102, 104, 105, 108, 110, 120, 122, 123, 132, 143, 145

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OFFSET

1,1

COMMENTS

For more details on this type of expansion, see A233582.

The cases with aperiodic expansions are listed in A233593.

All the listed cases become periodic after just two leading terms (it is a conjecture that this behavior is general); the validity of their expansions was explicitly tested.

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(2) is {1, 2, 4, 4, 4, 4, 4, ...}, i.e., it has a periodic termination. Consequently, 2 is a term of this sequence.

PROG

(PARI) See the link.

CROSSREFS

Cf. A233593.

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

Sequence in context: A167056 A131614 A275202 * A320773 A138390 A257804

Adjacent sequences: A233589 A233590 A233591 * A233593 A233594 A233595

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Jan 06 2014

STATUS

approved