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 A041226 Numerators of continued fraction convergents to sqrt(125). 10
 11, 56, 67, 123, 682, 15127, 76317, 91444, 167761, 930249, 20633239, 104096444, 124729683, 228826127, 1268860318, 28143753123, 141987625933, 170131379056, 312119004989, 1730726404001, 38388099893011, 193671225869056, 232059325762067, 425730551631123 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Johannes W. Meijer, Jun 12 2010: (Start) The a(n) terms of this sequence can be constructed with the terms of sequence A001946. For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. We observe that its period is five. (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1364,0,0,0,0,1). FORMULA From Johannes W. Meijer, Jun 12 2010: (Start) a(5n)   = A001946(3n+1), a(5n+1) = (A001946(3n+2) - A001946(3n+1))/2, a(5n+2) = (A001946(3n+2) + A001946(3n+1))/2, a(5n+3) = A001946(3n+2), a(5n+4) = A001946(3n+3)/2. (End) G.f.: -(x^9 -11*x^8 +56*x^7 -67*x^6 +123*x^5 +682*x^4 +123*x^3 +67*x^2 +56*x +11) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - Colin Barker, Nov 08 2013 MATHEMATICA Numerator[Convergents[Sqrt[125], 30]] (* Vincenzo Librandi, Oct 31 2013 *) CROSSREFS Cf. A041227, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550. Sequence in context: A206528 A259193 A099532 * A042503 A223766 A265151 Adjacent sequences:  A041223 A041224 A041225 * A041227 A041228 A041229 KEYWORD nonn,cofr,frac,easy AUTHOR EXTENSIONS More terms from Colin Barker, Nov 08 2013 STATUS approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)