A041481 -id:A041481 - cp's OEIS frontend

A040240 Continued fraction for sqrt(257).

16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32

Offset: 0

N. J. A. Sloane

			16 + 1/(32 + 1/(32 + 1/(32 + 1/(32 + ...)))) = sqrt(257).

Cf. A041480/A041481 (convergents).

Cf. A040000, A040002, A040012, A040056.

with(numtheory): Digits := 300: convert(evalf(sqrt(257)),confrac);

Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[257],100]] (* or *) PadRight[{16},100,{32}] (* Harvey P. Dale, Aug 15 2021 *)

a(n)=if(n,32,16) \\ Charles R Greathouse IV, Apr 08 2012

From Elmo R. Oliveira, Feb 13 2024: (Start)
a(n) = 32 for n >= 1.
G.f.: 16*(1+x)/(1-x).
E.g.f.: 32*exp(x) - 16.
a(n) = 16*A040000(n) = 8*A040002(n) = 4*A040012(n) = 2*A040056(n). (End)

A041480 Numerators of continued fraction convergents to sqrt(257).

Original entry on oeis.org

16, 513, 16432, 526337, 16859216, 540021249, 17297539184, 554061275137, 17747258343568, 568466328269313, 18208669762961584, 583245898743040001, 18682077429540241616, 598409723644030771713, 19167793234038524936432, 613967793212876828737537

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (32,1).

Cf. A041481.

Numerator[Convergents[Sqrt[257],40]] (* or *) LinearRecurrence[{32,1},{16,513},40] (* Harvey P. Dale, Aug 13 2012 *)

a(n) = 32*a(n-1)+a(n-2), n>1 ; a(0)=16, a(1)=513. G.f.: (16+x)/(1-32*x-x^2). - Philippe Deléham, Nov 23 2008

Additional term from Colin Barker, Nov 07 2013

cp's OEIS Frontend

A040240 Continued fraction for sqrt(257).

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