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 A288185 Least even number k such that the continued fraction for sqrt(k) has period n. 2
 2, 6, 130, 14, 74, 22, 58, 44, 106, 86, 298, 46, 746, 134, 1066, 94, 1018, 424, 922, 268, 394, 166, 586, 382, 1306, 214, 1354, 334, 1642, 436, 2122, 508, 1114, 454, 4138, 478, 3194, 1108, 4874, 526, 3418, 724, 2458, 604, 9914, 694, 4618, 844, 2746, 1318 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Periodic Continued Fraction FORMULA A003285(a(n)) = n, A000035(a(n)) = 0. EXAMPLE a(2) = 6, sqrt(6) = 2 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/...)))), period 2: [2, 4]. PROG (Python) from sympy import continued_fraction_periodic def A288185(n): d = 2 while True: s = continued_fraction_periodic(0, 1, d)[-1] if isinstance(s, list) and len(s) == n: return d d += 2 # Chai Wah Wu, Jun 08 2017 CROSSREFS Cf. A000035, A003285, A010337-A010339, A013642-A013644, A013646, A013943, A020347-A020439, A097853, A240072, A288184. Sequence in context: A060001 A181316 A101753 * A359961 A274695 A156515 Adjacent sequences: A288182 A288183 A288184 * A288186 A288187 A288188 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 06 2017 STATUS approved

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Last modified July 19 04:35 EDT 2024. Contains 374388 sequences. (Running on oeis4.)