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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114051 x such that x^2 - 23*y^2 = 1. 4
1, 24, 1151, 55224, 2649601, 127125624, 6099380351, 292643131224, 14040770918401, 673664360952024, 32321848554778751, 1550775066268428024, 74404881332329766401, 3569883528885560359224, 171280004505174567476351, 8217870332719493678505624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A Pellian equation (Pell's equation). - Benoit Cloitre, Feb 03 2006

Numbers n such that 23*(n^2-1) is a square. - Vincenzo Librandi, Nov 13 2010

LINKS

Colin Barker, Table of n, a(n) for n = 0..594

Tanya Khovanova, Recursive Sequences

John Robertson, Home page.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (48,-1).

FORMULA

a(0)=1, a(1)=24 then a(n) = 48*a(n-1)-a(n-2). - Benoit Cloitre, Feb 03 2006

G.f.: (1-24*x)/(1-48*x+x^2). - Philippe Deléham, Nov 18 2008

a(n) = T(n, 24) = (S(n, 48) - S(n-2, 48))/2, n >= 0, with Chebyshev's T- and S-polynomials (A049310 and A053120). - Wolfdieter Lang, Jul 02 2013

PROG

(PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))

(PARI) a0=1; a1=24; for(n=2, 30, a2=48*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre, Feb 03 2006

(PARI) Vec((1-24*x)/(1-48*x+x^2) + O(x^20)) \\ Colin Barker, Jun 13 2015

(MAGMA) [n: n in [1..10000000] |IsSquare(23*(n^2-1))] - Vincenzo Librandi, Nov 13 2010

CROSSREFS

Sequence in context: A130552 A160260 A268149 * A269092 A010562 A080775

Adjacent sequences:  A114048 A114049 A114050 * A114052 A114053 A114054

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Feb 01 2006

EXTENSIONS

More terms from Benoit Cloitre, Feb 03 2006

More terms from Robert G. Wilson v, Mar 17 2006

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 23 01:18 EDT 2017. Contains 285313 sequences.