This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063732 #23 Oct 02 2022 20:53:10 %S A063732 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 A063732 34,36,37,39,40,41,43,44,45,47,48,50,51,52,54,55,57,58,59,61,62,63,65, %U A063732 66,68,69,70,72,73,75,76,77,79,80,81,83,84,86,87,88,90 %N A063732 Numbers whose Lucas representation excludes L_0 = 2. %C A063732 From _Michel Dekking_, Aug 26 2019: (Start) %C A063732 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 A063732 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 A063732 It follows that a(n) = 3*n - floor(n*phi) - 2. %C A063732 (End) %F A063732 a(n) = floor((3-phi)*n)-1, where phi is the golden mean. - _Michel Dekking_, Aug 26 2019 %Y A063732 Cf. A003622, A022342. Complement of A054770. %Y A063732 Partial sums of A003842. %Y A063732 Cf. A130310 (Lucas representation). %K A063732 nonn %O A063732 1,3 %A A063732 _Fred Lunnon_, Aug 25 2001