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A040043 Continued fraction for sqrt(51). 4
7, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (0, 1).

FORMULA

a(n) = (1/2)*(21 + 7*(-1)^n) - 7*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 09 2009

EXAMPLE

7.1414284285428499979993998... = 7 + 1/(7 + 1/(14 + 1/(7 + 1/(14 + ...)))). - Harry J. Smith, Jun 06 2009

MAPLE

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

MATHEMATICA

ContinuedFraction[Sqrt[51], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 41000); x=contfrac(sqrt(51)); for (n=0, 20000, write("b040043.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

CROSSREFS

Cf. A010504 Decimal expansion. - Harry J. Smith, Jun 06 2009

Sequence in context: A109539 A109541 A173314 * A003872 A168374 A112438

Adjacent sequences:  A040040 A040041 A040042 * A040044 A040045 A040046

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 18 15:26 EDT 2019. Contains 325143 sequences. (Running on oeis4.)