A288186 - OEIS

A288186

Numbers k such that the continued fractions for sqrt(k) and sqrt(k+1) have the same period.

11, 21, 32, 33, 38, 39, 78, 83, 91, 95, 104, 111, 115, 140, 141, 146, 147, 161, 164, 204, 205, 206, 219, 222, 227, 230, 242, 245, 299, 310, 320, 321, 326, 327, 340, 344, 371, 383, 395, 404, 413, 428, 434, 438, 443, 447, 451, 452, 464, 471, 498, 504, 515, 539, 545, 572, 573, 578, 579, 594, 596, 644, 654, 659, 695

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OFFSET

1,1

COMMENTS

Numbers k such that A003285(k) = A003285(k+1).

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Periodic Continued Fraction

EXAMPLE

11 is in the sequence because sqrt(11) = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + 1/...)))), period 2: [3, 6] and sqrt(12) = 3 + 1/(2 + 1/(6 + 1/(2 + 1/(6 + 1/...)))), period 2: [2, 6].

CROSSREFS

Cf. A003285, A013943, A031400, A097853.

Sequence in context: A178205 A239464 A180105 * A264646 A139113 A109335

Adjacent sequences: A288183 A288184 A288185 * A288187 A288188 A288189

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 06 2017

STATUS

approved