A114049 x such that x^2 - 21*y^2 = 1.

1, 55, 6049, 665335, 73180801, 8049222775, 885341324449, 97379496466615, 10710859270003201, 1178097140203885495, 129579974563157401249, 14252619104807110251895, 1567658521554218970307201

Offset: 0

Author

Cino Hilliard, Feb 01 2006

Keywords

• easy
• nonn

Comments

This sequence is computed with g(1e9,21) in the PARI program.

A Pellian equation - Benoit Cloitre, Feb 03 2006

Numbers m such that 21*(m^2-1) is square. - Vincenzo Librandi, Nov 13 2010

Examples

			(55^2-1)/21 = 12^2
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..489 (terms 0..130 from Vincenzo Librandi)
• Tanya Khovanova, Recursive Sequences
• John Robertson, Home page.
• Index entries for linear recurrences with constant coefficients, signature (110, -1).

Programs

Mathematica

Table[ Numerator@ FromContinuedFraction@ ContinuedFraction[Sqrt@21, Length@ Last@ ContinuedFraction@ Sqrt@21*n], {n, 12}] (* Robert G. Wilson v, Feb 28 2006 *)
LinearRecurrence[{110,-1},{1,55},20] (* Harvey P. Dale, Jan 27 2013 *)

PARI

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

PARI

a0=1;a1=55;for(n=2,30,a2=110*a1-a0;a0=a1;a1=a2;print1(a2,",")) \\ Benoit Cloitre

Formula

a(0)=1, a(1)=55, a(n)=110*a(n-1)-a(n-2). - Benoit Cloitre, Feb 03 2006

G.f.: (1-55*x)/(1-110*x+x^2). - Philippe Deléham, Nov 18 2008

Extensions

More terms from Benoit Cloitre, Feb 03 2006