|
Search: id:A156841
|
|
| |
|
| 46, 263, 1538, 3871, 7262, 11711, 17218, 23783, 31406, 40087, 49826, 60623, 72478, 85391, 99362, 114391, 130478, 147623, 165826, 185087, 205406, 226783, 249218, 272711, 297262, 322871, 349538, 377263, 406046, 435887, 466786, 498743, 531758
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.
Let n=[A156849] (156,373,685,902,...,) =n^2-2=0 mod (23^2). If A=[A156841] (46,263,1538,3871,.,) = 529*n^2-312*n+46 or A=[156842] (263,46,887,2787) =(529*n^2-746*n+263 , Y=23*n, or [A156845] (3588,15755,27922,...,) = 12167*n-8579, or Y=[A156846] (8579,20746,32913,...,) =12167*n-3588, and X=279841*n^2-165048*n+24335 [A156843] (24335,139128,813603,...,) or X=[A156844] =279841*n^2-394634*n+139128 (139128,24335,469224,1473795,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=156, A=46, Y=3588, X=24335, 24335^2-46*3588^2=1 ; n=373, A=263, Y=8579, X=139128; 139128^2-263*8579^2=1; n=685, A=887, Y=15755, X=469224; 469224^2-887*15755^2=1; n=902, A=1538, Y=20746, X=813603; 813603^2-1538*20746^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
|
|
LINKS
|
Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
|
|
EXAMPLE
|
For n=0, a(0)=46; n=1, a(1)=263; n=2, a(2)=1538
|
|
CROSSREFS
|
Cf. A156842
Cf. A156843, A156844, A156845, A156846, A156849 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A160334 A083358 A026913 this_sequence A086979 A077734 A135735
Adjacent sequences: A156838 A156839 A156840 this_sequence A156842 A156843 A156844
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 17 2009
|
|
|
Search completed in 0.002 seconds
|
