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%I #24 Mar 23 2019 02:39:31
%S 5,11,17,25,38,57,87,135,213,337,537,860,1382,2226,3591,5800,9372,
%T 15151,24501,39629,64106,103710,167790,271473,439235,710679,1149884,
%U 1860533,3010385,4870884,7881234,12752082,20633279,33385323,54018563,87403846,141422368
%N Sum of n-th Lucas number greater than 3 and n-th number that is 1 or is not a Fibonacci number.
%F a(n) = phi^(n+2) + n + log_phi(n) + O(1), where phi = 1/2 + sqrt(5)/2 is the golden ratio. - _Charles R Greathouse IV_, Jan 17 2012
%F a(n) = A000032(n+2) + A001690(n-1), n >= 2. - _R. J. Mathar_, Feb 01 2019
%t nMax = 50; With[{luke = LucasL[Range[3, nMax + 2]], dn = Take[Join[{1}, Complement[Range[2nMax], Fibonacci[Range[2nMax]]]], nMax]}, Total /@ Thread[{luke, nMax}]] (* _Harvey P. Dale_, Jan 17 2012 *)
%o (PARI) b(n)=fibonacci(n+1)+fibonacci(n+3)
%o d(n)=my(k=2);n-=3;while(fibonacci(k++)<=n+k,);n+k
%o a(n)=b(n)+d(n) \\ _Charles R Greathouse IV_, Jan 17 2012
%K nonn
%O 1,1
%A _Clark Kimberling_
%E a(28)-a(37) corrected by _Harvey P. Dale_, Jan 17 2012