|
|
A114048
|
|
x-values in the solution to x^2 - 19*y^2 = 1.
|
|
4
|
|
|
1, 170, 57799, 19651490, 6681448801, 2271672940850, 772362118440199, 262600848596726810, 89283516160768675201, 30356132893812752841530, 10320995900380175197444999, 3509108249996365754378458130
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This sequence is computed with g(1e9,19) in the PARI program.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 340*a(n-1) - a(n-2) for n >= 3; a(1)=1, a(2)=170. - Benoit Cloitre, Feb 03 2006
|
|
EXAMPLE
|
(170^2 - 1)/19 = 39^2.
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))
(PARI) a(n)=real((170+39*quadgen(4*19))^n) /* Michael Somos, Feb 15 2006 */
(PARI) a=vector(12); a[1]=1; a[2]=170; for(i=3, #a, a[i]=340*a[i-1]-a[i-2]); a \\ Benoit Cloitre
(Magma) I:=[1, 170]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Dec 21 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|