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 A195680 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(12). 4
 7, 2772, 5945, 26144, 285621, 257076560, 2386970016, 103850955649, 254621037540, 3060691213613, 29733959304728, 62837775720000, 89511043811115, 453985767379732, 1567652657852541, 35830073055128140, 22926879590846577132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A195500 for a discussion and references. LINKS MATHEMATICA r = Sqrt[12]; z = 24; p[{f_, n_}] := (#1[[2]]/#1[[ 1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[ 2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[ Array[FromContinuedFraction[ ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]]; {a, b} = ({Denominator[#1], Numerator[#1]} &)[ p[{r, z}]] (* A195680, A195681 *) Sqrt[a^2 + b^2] (* A195682 *) (* Peter J. C. Moses, Sep 02 2011 *) CROSSREFS Cf. A195500, A195681, A195682. Sequence in context: A354027 A178172 A234621 * A203587 A077721 A235464 Adjacent sequences: A195677 A195678 A195679 * A195681 A195682 A195683 KEYWORD nonn AUTHOR Clark Kimberling, Sep 22 2011 STATUS approved

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Last modified January 30 12:01 EST 2023. Contains 359943 sequences. (Running on oeis4.)