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%I #10 Nov 26 2020 23:02:38
%S 9,25,27,49,81,121,169,175,225,243,289,325,361,529,637,729,961,1225,
%T 1331,1369,1539,1681,1849,2025,2209,2809,3025,3481,3721,4225,4489,
%U 5041,5329,5929,6241,6721,6889,6929,7921,8281,9409
%N Odd composite integers m such that A087130(m-J(m,29)) == 2*J(m,29) (mod m), where J(m,29) is the Jacobi symbol.
%C The generalized Pell-Lucas sequences of integer parameters (a,b) defined by V(m+2)=a*V(m+1)-b*V(m) and V(0)=2, V(1)=a, satisfy the identity
%C V(p-J(p,D)) == 2*J(p,D) (mod p) when p is prime, b=-1 and D=a^2+4.
%C This sequence has the odd composite integers with V(m-J(m,D)) == 2*J(m,D) (mod m).
%C For a=5 and b=-1, we have D=29 and V(m) recovers A087130(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)
%t Select[Range[3, 10000, 2], CompositeQ[#] && Divisible[LucasL[# - (j = JacobiSymbol[#, 29]), 5] - 2*j, #] &] (* _Amiram Eldar_, Nov 26 2020 *)
%Y Cf. A087130.
%Y Cf. A339125 (a=1, b=-1), A339126 (a=3, b=-1), A339128 (a=7, b=-1), A339129 (a=3, b=1), A339130 (a=5, b=1), A339131 (a=7, b=1).
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Nov 24 2020
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