login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A266698 x-values of solutions to the Diophantine equation x^2 - 7*y^2 = 2. 2
3, 45, 717, 11427, 182115, 2902413, 46256493, 737201475, 11748967107, 187246272237, 2984191388685, 47559815946723, 757972863758883, 12080006004195405, 192522123203367597, 3068273965249686147, 48899861320791610755, 779329507167416085933, 12420372253357865764173, 197946626546558436140835 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A159678 gives the y-values of solutions to the Diophantine equation x^2 - 7*y^2 = 2.

LINKS

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (16,-1).

FORMULA

a(1)=3, a(2)=45, a(n) = 16*a(n-1) - a(n-2).

a(n) = A041008(4n-2). - Robert Israel, Jan 05 2016

G.f.: -3*x*(x-1) / ( 1-16*x+x^2 ). a(n) = 3*A157456(n). - R. J. Mathar, Jan 12 2016

MATHEMATICA

LinearRecurrence[{16, -1}, {3, 45}, 20 ]

PROG

(PARI) lista(nn) = {print1(x = 3, ", "); print1(y = 45, ", "); for (n=2, nn, z = 16*y - x; print1(z, ", "); x = y; y = z; ); } \\ Michel Marcus, Jan 05 2016

(MAGMA) [n: n in [1..2*10^7] | IsSquare((n^2-2)/7)]; // Vincenzo Librandi, Jan 06 2016

CROSSREFS

Cf. A159678.

Sequence in context: A131568 A287031 A124487 * A132303 A298799 A202437

Adjacent sequences:  A266695 A266696 A266697 * A266699 A266700 A266701

KEYWORD

nonn,easy

AUTHOR

Sture Sjöstedt, Jan 03 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 05:43 EDT 2019. Contains 325168 sequences. (Running on oeis4.)