A041021 -id:A041021 - cp's OEIS frontend

A010471 Decimal expansion of square root of 14.

3, 7, 4, 1, 6, 5, 7, 3, 8, 6, 7, 7, 3, 9, 4, 1, 3, 8, 5, 5, 8, 3, 7, 4, 8, 7, 3, 2, 3, 1, 6, 5, 4, 9, 3, 0, 1, 7, 5, 6, 0, 1, 9, 8, 0, 7, 7, 7, 8, 7, 2, 6, 9, 4, 6, 3, 0, 3, 7, 4, 5, 4, 6, 7, 3, 2, 0, 0, 3, 5, 1, 5, 6, 3, 0, 6, 9, 3, 9, 0, 2, 7, 9, 7, 6, 8, 0, 9, 8, 9, 5, 1, 9, 4, 3, 7, 9, 5, 7

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 3 followed by {1, 2, 1, 6} repeated. - Harry J. Smith, Jun 02 2009

The convergents are given in A041020/A041021. - Wolfdieter Lang, Nov 27 2017

			3.741657386773941385583748732316549301756019807778726946303745467320035...

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2

Cf. A010123 (continued fraction), A041020/A041021.

evalf[100](sqrt(14)); # Muniru A Asiru, Feb 12 2019

RealDigits[N[Sqrt[14], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)
RealDigits[Sqrt[14],10,120][[1]] (* Harvey P. Dale, Jan 07 2023 *)

default(realprecision, 20080); x=sqrt(14); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010471.txt", n, " ", d));  \\ Harry J. Smith, Jun 02 2009

A041020 Numerators of continued fraction convergents to sqrt(14).

Original entry on oeis.org

3, 4, 11, 15, 101, 116, 333, 449, 3027, 3476, 9979, 13455, 90709, 104164, 299037, 403201, 2718243, 3121444, 8961131, 12082575, 81456581, 93539156, 268534893, 362074049, 2440979187, 2803053236, 8047085659

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,30,0,0,0,-1).

Cf. A010471, A041021.

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[14],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011*)

G.f.: (3+4*x+11*x^2+15*x^3+11*x^4-4*x^5+3*x^6-x^7)/(1-30*x^4+x^8). - Colin Barker, Jan 03 2012

a(n) = 30*a(n-4) - a(n-8). - Wesley Ivan Hurt, Aug 04 2025

cp's OEIS Frontend

A010471 Decimal expansion of square root of 14.

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