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%I #23 Oct 02 2022 20:53:10
%S 0,1,3,4,5,7,8,10,11,12,14,15,16,18,19,21,22,23,25,26,28,29,30,32,33,
%T 34,36,37,39,40,41,43,44,45,47,48,50,51,52,54,55,57,58,59,61,62,63,65,
%U 66,68,69,70,72,73,75,76,77,79,80,81,83,84,86,87,88,90
%N Numbers whose Lucas representation excludes L_0 = 2.
%C From _Michel Dekking_, Aug 26 2019: (Start)
%C This sequence is a generalized Beatty sequence. We know that A054770, the sequence of numbers whose Lucas representation includes L_0=2, is equal to A054770(n) = A000201(n) + 2*n - 1 = floor((phi+2)*n) - 1.
%C One also easily checks that the numbers 3-phi and phi+2 form a Beatty pair. This implies that the sequence with terms floor((3-phi)*n)-1 is the complement of A054770 in the natural numbers 0,1,2,...
%C It follows that a(n) = 3*n - floor(n*phi) - 2.
%C (End)
%F a(n) = floor((3-phi)*n)-1, where phi is the golden mean. - _Michel Dekking_, Aug 26 2019
%Y Cf. A003622, A022342. Complement of A054770.
%Y Partial sums of A003842.
%Y Cf. A130310 (Lucas representation).
%K nonn
%O 1,3
%A _Fred Lunnon_, Aug 25 2001
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