|
|
A337627
|
|
Odd composite integers m such that U(m)^2 == 1 (mod m) and V(m) == 4 (mod m), where U(m) and V(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=4 and b=-1, respectively.
|
|
4
|
|
|
9, 161, 341, 897, 901, 1281, 1853, 2737, 4181, 4209, 4577, 5473, 5611, 5777, 6119, 6721, 9701, 9729, 10877, 11041, 12209, 12349, 13201, 13481, 14981, 15251, 16771, 19669, 20591, 20769, 20801, 23323, 27403, 27613, 28421, 29281, 29489, 32929, 33001, 34561, 38801
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
For a,b integers, the following sequences are defined:
generalized Lucas sequences by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1,
generalized Pell-Lucas sequences by V(n+2)=a*V(n+1)-b*V(n) and V(0)=2, V(1)=a.
These satisfy the identities U(p)^2 == 1 and V(p)==a (mod p) for p prime and b=1,-1.
These numbers may be called weak generalized Lucas-Bruckner pseudoprimes of parameters a and b.The current sequence is defined for a=4 and b=-1.
|
|
LINKS
|
|
|
MATHEMATICA
|
Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 4]*Fibonacci[#, 4] - 1, #] && Divisible[LucasL[#, 4] - 4, #] &]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|