%I #8 Jan 01 2021 14:35:11
%S 9,15,25,27,45,75,91,121,125,135,143,147,175,225,275,325,375,441,483,
%T 625,675,735,755,1125,1323,1547,1573,1875,1935,2015,2205,2275,2485,
%U 2943,3025,3125,3375,3575,3675,3775,3843,4375,5525,5625,5819,6543,6615,6721
%N Odd composite integers m such that A052918(2*m-J(m,29)) == 1 (mod m), where J(m,29) is the Jacobi symbol.
%C The generalized Lucas sequences of integer parameters (a,b) defined by U(m+2)=a*U(m+1)-b*U(m) and U(0)=0, U(1)=1, satisfy U(2*p-J(p,D)) == 1 (mod p) whenever p is prime, k is a positive integer, b=-1 and D=a^2+4.
%C The composite integers m with the property U(k*m-J(m,D)) == U(k-1) (mod m) are called generalized Lucas pseudoprimes of level k- and parameter a. Here b=-1, a=5, D=29 and k=2, while U(m) is A052918(m).
%D D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020.
%D D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021).
%D D. Andrica, O. Bagdasar, On generalized pseudoprimality of level k (submitted).
%H Dorin Andrica, Vlad Crişan, and Fawzi Al-Thukair, <a href="https://doi.org/10.1016/j.ajmsc.2017.06.002">On Fibonacci and Lucas sequences modulo a prime and primality testing</a>, Arab Journal of Mathematical Sciences, 2018, 24(1), 9--15.
%t Select[Range[3, 15000, 2], CoprimeQ[#, 29] && CompositeQ[#] && Divisible[Fibonacci[2*#-JacobiSymbol[#, 29], 5] - 1, #] &]
%Y Cf. A052918, A071904, A340095 (a=5, b=-1, k=1).
%Y Cf. A340118 (a=1, b=-1, k=2), A340119 (a=3, b=-1, k=2), A340121 (a=7, b=-1, k=2).
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Dec 28 2020