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 A041008 Numerators of continued fraction convergents to sqrt(7). 11
 2, 3, 5, 8, 37, 45, 82, 127, 590, 717, 1307, 2024, 9403, 11427, 20830, 32257, 149858, 182115, 331973, 514088, 2388325, 2902413, 5290738, 8193151, 38063342, 46256493, 84319835, 130576328, 606625147, 737201475, 1343826622, 2081028097, 9667939010, 11748967107, 21416906117 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 C. Elsner, Series of Error Terms for Rational Approximations of Irrational Numbers , J. Int. Seq. 14 (2011) # 11.1.4. C. Elsner, M. Stein, On Error Sum Functions Formed by Convergents of Real Numbers, J. Int. Seq. 14 (2011) # 11.8.6. Index entries for linear recurrences with constant coefficients, signature (0,0,0,16,0,0,0,-1). FORMULA G.f.: (2 + 3*x + 5*x^2 + 8*x^3 + 5*x^4 - 3*x^5 + 2*x^6 - x^7)/(1 - 16*x^4 + x^8). MATHEMATICA Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[7], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *) Numerator[Convergents[Sqrt[7], 30]] (* Vincenzo Librandi, Oct 28 2013 *) PROG From M. F. Hasler, Nov 01 2019: (Start) (PARI) A041008=contfracpnqn(c=contfrac(sqrt(7)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n)=A041008[n+1]! For more terms use: A041008(n)={n<#A041008|| A041008=extend(A041008, [4, 16; 8, -1], n\.8); A041008[n+1]} extend(A, c, N)={for(n=#A+1, #A=Vec(A, N), A[n]=[A[n-i]|i<-c[, 1]]*c[, 2]); A} \\ (End) CROSSREFS Cf. A010465, A041009 (denominators), A266698 (quadrisection), A001081 (quadrisection). Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041010 (m=8), A005667 (m=10), A041014 (m=11), A041016 (m=12), ..., A042934 (m=999), A042936 (m=1000). Sequence in context: A281618 A059359 A042069 * A041569 A268480 A128485 Adjacent sequences:  A041005 A041006 A041007 * A041009 A041010 A041011 KEYWORD nonn,cofr,frac,easy AUTHOR STATUS approved

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)