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A335672 Odd composite integers m such that A005248(m) == 3 (mod m).

%I A335672 #17 Nov 23 2023 12:02:54
%S A335672 15,105,195,231,323,377,435,665,705,1443,1551,1891,2465,2737,2849,
%T A335672 3289,3689,3745,3827,4181,4465,4879,5655,5777,6479,6601,6721,7055,
%U A335672 7743,8149,9879,10815,10877,11305,11395,11663,12935,13201,13981,15251,15301,17119,17261,17711,18407,18915,19043,20999
%N A335672 Odd composite integers m such that A005248(m) == 3 (mod m).
%C A335672 If p is a prime, then A005248(p)==3 (mod p).
%C A335672 This sequence contains the odd composite integers for which the congruence holds.
%C A335672 The generalized Pell-Lucas sequences of integer parameters (a,b) defined by V(n+2)=a*V(n+1)-b*V(n) and V(0)=2, V(1)=a, satisfy the identity V(p)==a (mod p) whenever p is prime and b=-1,1.
%C A335672 For a=3, b=1, V(n) recovers A005248(n) (bisection of Fibonacci numbers).
%D A335672 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020).
%H A335672 Chai Wah Wu, <a href="/A335672/b335672.txt">Table of n, a(n) for n = 1..1000</a>
%H A335672 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 A335672 15 is the first odd composite integer for which A005248(15)=18604984==3 (mod 15).
%t A335672 Select[Range[3, 10000, 2], CompositeQ[#] && Divisible[LucasL[2#] - 3, #] &] (* _Amiram Eldar_, Jun 18 2020 *)
%Y A335672 Cf. A005248, A335669 (a=3,b=-1), A335673 (a=4,b=1), A335674 (a=5,b=1).
%K A335672 nonn
%O A335672 1,1
%A A335672 _Ovidiu Bagdasar_, Jun 17 2020