A187415 - OEIS

%I #7 Feb 10 2014 21:32:05

%S 1,3,4,6,8,10,11,13,15,17,18,20,22,23,25,27,29,30,32,34,35,37,39,40,

%T 42,44,46,47,49,51,53,54,56,58,60,61,63,64,67,68,70,71,73,75,77,78,80,

%U 82,83,85,87,89,91,92,93,96,97,99,101,103,104,106,107,110,111,113,114,117,118,120,121,123,125,126,128,130,132,133,135,137,139,140,142,143,146,147,149,151

%N Rank transform of the sequence floor(n*(-1+sqrt(5))); complement of A187416.

%C See A187224.

%t m = -1+5^(1/2);

%t seqA = Table[Floor[m*n], {n, 1, 180}]  (* A001961 *)

%t seqB = Table[n, {n, 1, 80}];                   (* A000027 *)

%t jointRank[{seqA_, seqB_}] := {Flatten@Position[#1, {_, 1}],

%t Flatten@Position[#1, {_, 2}]} &[Sort@Flatten[{{#1, 1} & /@ seqA,

%t {#1, 2} & /@ seqB}, 1]];

%t limseqU = FixedPoint[jointRank[{seqA, #1[[1]]}] &, jointRank

%t [{seqA, seqB}]][[1]]                                      (* A187415 *)

%t Complement[Range[Length[seqA]], limseqU]  (* A187416 *)

%t (* by _Peter J. C. Moses_, Mar 09 2011 *)

%Y Cf. A187224, A187416.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 09 2011