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

Offset: 1

Author

Ilya Gutkovskiy, Jun 06 2017

Keywords

• nonn

Comments

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

Examples

			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].
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Periodic Continued Fraction

Crossrefs

Cf. A003285, A013943, A031400, A097853.