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A188012 Positions of 0 in A188011; complement of A188013.

%I A188012 #19 Sep 08 2022 08:45:56
%S A188012 3,8,16,21,29,37,42,50,55,63,71,76,84,92,97,105,110,118,126,131,139,
%T A188012 144,152,160,165,173,181,186,194,199,207,215,220,228,236,241,249,254,
%U A188012 262,270,275,283,288,296,304,309,317,325,330,338,343,351,359,364,372,377,385,393,398,406,414,419,427,432,440
%N A188012 Positions of 0 in A188011; complement of A188013.
%C A188012 See A188014 and A188011.
%H A188012 G. C. Greubel, <a href="/A188012/b188012.txt">Table of n, a(n) for n = 1..5000</a>
%F A188012 a(n+1) = 3*floor(n*phi)+2*n+3 for n>=0, where phi = (1+sqrt(5))/2 (see A188011). - _Michel Dekking_, Sep 28 2017
%t A188012 r=(1+5^(1/2))/2; k=3;
%t A188012 t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}]   (* A188011 *)
%t A188012 Flatten[Position[t,0]]  (* A188012 *)
%t A188012 Flatten[Position[t,1]]  (* A188013 *)
%t A188012 Table[3*Floor[(n-1)*GoldenRatio] + 2*n + 1, {n, 1, 65}] (* _G. C. Greubel_, Nov 22 2018 *)
%o A188012 (PARI) vector(65, n, 3*floor((n-1)*(1+sqrt(5))/2)+2*n+1) \\ _G. C. Greubel_, Nov 22 2018
%o A188012 (Magma) [3*Floor((n-1)*(1+Sqrt(5))/2)+2*n+1: n in [1..65]]; // _G. C. Greubel_, Nov 22 2018
%o A188012 (Sage) [3*floor((n-1)*(1+sqrt(5))/2)+2*n+1 for n in (1..65)] # _G. C. Greubel_, Nov 22 2018
%Y A188012 Cf. A188011, A188013, A188014.
%K A188012 nonn
%O A188012 1,1
%A A188012 _Clark Kimberling_, Mar 19 2011