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%I #12 Apr 21 2022 09:15:05
%S 1,4,18,76,123,322,843,1364,5778,15127,24476,39603,64079,103682,
%T 167761,271443,439204,710647,1149851,1860498,4870847,7881196,12752043,
%U 20633239,33385282,87403803,141422324,228826127,599074578,969323029,1568397607,2537720636,4106118243,10749957122,17393796001,28143753123
%N Nonprime Lucas numbers.
%C A Lucas number L(n) has for multiples L(m) those for which m = n mod 2n.
%C However, there are composite Lucas numbers with prime indices in the sequence of Lucas numbers; these are coprime to smaller Lucas numbers (such as L(23) and L(29), which have for least prime factor 139 and 59, respectively.
%C L(m)|L(n) if and only if n = (2k - 1)m, with m > 1 and k > 0 (this is Theorem 16.6 in Koshy's book).
%D Thomas Koshy, Fibonacci and Lucas Numbers with Applications. New York: John Wiley & Sons Inc. (2001) p. 200
%H G. C. Greubel, <a href="/A172159/b172159.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[LucasL[Range[60]],Not[PrimeQ[#]]&]
%o (Magma) [Lucas(n): n in [1..60] | not IsPrime(Lucas(n)) ]; // _G. C. Greubel_, Apr 21 2022
%o (SageMath) [lucas_number2(n,1,-1) for n in (1..60) if not is_prime(lucas_number2(n,1,-1))] # _G. C. Greubel_, Apr 21 2022
%Y Cf. A000032 (Lucas numbers), A002808 (composite numbers).
%K nonn
%O 1,2
%A _Alonso del Arte_, Nov 19 2010
%E Terms a(27) onward added by _G. C. Greubel_, Apr 21 2022
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