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%I #40 Nov 23 2023 12:02:43
%S 4,8,16,24,32,48,64,72,96,120,128,144,168,192,216,240,256,264,272,288,
%T 336,360,384,432,480,504,512,528,544,576,600,648,672,720,768,792,816,
%U 840,864,960,1008,1024,1056,1080,1088,1152,1176,1200,1296,1320,1344,1440,1512
%N Even composites m such that A002203(m) == 2 (mod m).
%C If p is a prime, then A002203(p)==2 (mod p).
%C Even composites for which the congruence holds.
%C Even composites m for which the sum of the Pell numbers A000129(0) + ... + A000129(m-1) is divisible by m.
%D D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020).
%H Amiram Eldar, <a href="/A335668/b335668.txt">Table of n, a(n) for n = 1..10000</a>
%H 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).
%e 4 is the first composite number m for which A002203(m)==2 (mod m) since A002203(4)=34==2 (mod 4), so a(1)=4.
%e The next even composite for which the congruence holds is m = 8 since A002203(8)=1154==2 (mod 8), so a(2)=8.
%t Select[Range[4, 2000, 2], Divisible[LucasL[#, 2] - 2, #] &] (* _Amiram Eldar_, Jun 18 2020 *)
%Y Cf. A270342 (all positive integers), A270345 (all composites), A330276 (odd composites),
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Jun 17 2020
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