cp's OEIS Frontend

A337626 Odd composite integers m such that U(m)^2 == 1 (mod m) and V(m) == 3 (mod m), where U(m) and V(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=3 and b=-1, respectively.

%I A337626 #12 Nov 23 2023 13:17:35
%S A337626 33,119,385,561,649,1189,1441,2065,2289,2465,2849,4187,6545,12871,
%T A337626 13281,14041,16109,18241,22049,23479,24769,25345,28421,31631,34997,
%U A337626 38121,38503,41441,45961,48577,50545,53585,56279,58081,59081,61447,63393,66385,75077,91187
%N A337626 Odd composite integers m such that U(m)^2 == 1 (mod m) and  V(m) == 3 (mod m), where U(m) and V(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=3 and b=-1, respectively.
%C A337626 Intersection of A335669 and A337234.
%C A337626 For a,b integers, the following sequences are defined:
%C A337626 generalized Lucas sequences by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1,
%C A337626 generalized Pell-Lucas sequences by V(n+2)=a*V(n+1)-b*V(n) and V(0)=2, V(1)=a.
%C A337626 These satisfy the identities U(p)^2 == 1 and V(p)==a (mod p) for p prime and b=1,-1.
%C A337626 These numbers may be called weak generalized Lucas-Bruckner pseudoprimes of parameters a and b.The current sequence is defined for a=3 and b=-1.
%H A337626 D. Andrica and O. Bagdasar, <a href="https://repository.derby.ac.uk/item/92yqq/on-some-new-arithmetic-properties-of-the-generalized-lucas-sequences">On some new arithmetic properties of the generalized Lucas sequences</a>, preprint for Mediterr. J. Math. 18, 47 (2021).
%t A337626 Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 3]*Fibonacci[#, 3] - 1, #] && Divisible[LucasL[#, 3] - 3, #] &]
%Y A337626 Cf. A335669, A337234.
%K A337626 nonn
%O A337626 1,1
%A A337626 _Ovidiu Bagdasar_, Sep 19 2020
%E A337626 More terms from _Amiram Eldar_, Sep 19 2020