|
|
A081231
|
|
Let p = n-th prime of the form 4k+3, take smallest solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and y >= 1; sequence gives value of x.
|
|
4
|
|
|
2, 8, 10, 170, 24, 1520, 3482, 48, 530, 48842, 3480, 80, 82, 227528, 962, 4730624, 10610, 77563250, 1728148040, 64080026, 168, 4190210, 8994000, 16266196520, 278354373650, 224, 226, 6195120, 3674890, 139128, 115974983600, 138274082
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
For n=3, p = 11, x=10, y=3 since we have 10^2 = 11*3^2 + 1, so a(3) = 10.
|
|
MATHEMATICA
|
PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[ Sqrt[m]]; n = Length[ Last[cf]]; If[ OddQ[n], n = 2*n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; Transpose[ PellSolve /@ Select[ Prime[ Range[72]], Mod[ #, 4] == 3 &]][[1]] (* Robert G. Wilson v, Sep 02 2004 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|