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A288186 Numbers k such that the continued fractions for sqrt(k) and sqrt(k+1) have the same period. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that A003285(k) = A003285(k+1).
LINKS
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
Sequence in context: A178205 A239464 A180105 * A264646 A139113 A109335
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 06 2017
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)