|
Search: id:A121740
|
|
|
| A121740 |
|
Solutions to the Pell equation x^2 - 17y^2 = 1 (y values). |
|
+0
1
|
|
| 0, 8, 528, 34840, 2298912, 151693352, 10009462320, 660472819768, 43581196642368, 2875698505576520, 189752520171407952, 12520790632807348312, 826182429245113580640, 54515519539544688973928
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
After initial term this sequence bisects A041025. See A099370 for corresponding x values. a(n+1)/a(n) apparently converges to (4+sqrt(17))^2.
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Pell Equation
|
|
FORMULA
|
a(n)=((33+8*sqrt(17))^n - (33-8*sqrt(17))^n) / (2*sqrt(17)).
a(n) = 65*(a(n-1)+a(n-2))-a(n-3). a(n) = 67*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Feb 07 2007
|
|
EXAMPLE
|
A099370(1)^2 - 17*a(1)^2 = 33^2 - 17*8^2 = 1089 - 1088 = 1.
|
|
PROGRAM
|
(PARI) Program uses fact that continued fraction for sqrt(17) = [4, 8, 8, ...]. print1("0, "); forstep(n=2, 40, 2, v=vector(n, i, if(i>1, 8, 4)); print1(contfracpnqn(v)[2, 1], ", "))
|
|
CROSSREFS
|
Cf. A099370, A041025, A040012.
Sequence in context: A091112 A015480 A003397 this_sequence A089671 A112035 A027536
Adjacent sequences: A121737 A121738 A121739 this_sequence A121741 A121742 A121743
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 31 2006
|
|
|
Search completed in 0.002 seconds
|
