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%I #9 Dec 07 2020 18:22:56
%S 9,49,63,121,169,289,323,361,377,441,529,841,961,1127,1369,1681,1849,
%T 1891,2209,2303,2809,2961,3481,3721,3751,3827,4181,4489,4901,4961,
%U 5041,5329,5491,5777,6137,6241,6601,6721,6889,7381,7921,8149,9409,10201,10609,10877,10933,11449,11663
%N Odd composite integers m such that A005248(m-J(m,5)) == 2 (mod m), where J(m,5) 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 (mod p) when p is prime, b=1 and D=a^2-4.
%C This sequence contains the odd composite integers with V(m-J(m,D)) == 2 (mod m).
%C For a=3 and b=1, we have D=5 and V(m) recovers A005248(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, 12000, 2], CompositeQ[#] && Divisible[LucasL[2*(# - JacobiSymbol[#, 5])] - 2, #] &] (* _Amiram Eldar_, Nov 26 2020 *)
%Y Cf. A005248.
%Y Cf. A339125 (a=1, b=-1), A339126 (a=3, b=-1), A339127 (a=5, b=-1), A339128 (a=7, 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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