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 A062345 Length of period of continued fraction expansion of square root of 3^n-1. 1
 1, 2, 1, 2, 10, 2, 19, 2, 25, 2, 156, 2, 149, 2, 580, 2, 716, 2, 6461, 2, 2485, 2, 123256, 2, 64, 2, 8638, 2, 722190, 2, 3804214, 2, 1783536, 2, 3550696, 2, 86022946, 2, 22119349, 2, 692630166, 2, 8247763078, 2, 43380360, 2, 15150768502, 2, 10229872316, 2, 36580802370, 2, 333495606762, 2, 676122216162, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..56. FORMULA a(n) = A003285(A024023(n)). - Michel Marcus, Sep 25 2019 EXAMPLE The period of sqrt(242) contains 10 terms: [1,1,3,1,14,1,3,1,1,30] MAPLE with(numtheory): [seq(nops(cfrac(sqrt(3^k-1), 'periodic', 'quotients')[2]), k=1..16)]; MATHEMATICA Table[Length[Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 36}] CROSSREFS Cf. A003285, A024023, A059866, A059926, A059927, A062328. Sequence in context: A225432 A086382 A249416 * A077098 A069238 A248977 Adjacent sequences: A062342 A062343 A062344 * A062346 A062347 A062348 KEYWORD nonn,more AUTHOR Labos Elemer, Jul 13 2001 EXTENSIONS a(37)-a(42) from Vaclav Kotesovec, Aug 28 2019 a(43)-a(44) from Vaclav Kotesovec, Sep 17 2019 a(45)-a(52) from Chai Wah Wu, Sep 25 2019 a(53)-a(56) from Chai Wah Wu, Sep 29 2019 STATUS approved

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Last modified September 18 03:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)