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
D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).
MATHEMATICA
Select[Range[3, 10000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 2] - 4, #] && Divisible[ChebyshevU[#-1, 2]*ChebyshevU[#-1, 2] - 1, #] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Sep 20 2020
EXTENSIONS
More terms from Amiram Eldar, Sep 21 2020
STATUS
approved