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Rank transform of the sequence floor((4 - sqrt(5))*n); complement of A187908.
3

%I #14 Sep 09 2018 02:23:25

%S 1,3,5,7,9,11,13,15,16,19,20,23,24,26,28,30,32,34,36,38,40,41,43,46,

%T 48,49,51,53,55,57,59,61,63,64,66,68,71,73,74,76,78,80,82,84,86,88,89,

%U 91,93,95,97,99,101,103,105,107,109,111,113,114,116,118,120,122,124,126,128,130,132,134,136,138,139,141,143,145,147,149,151,153,155

%N Rank transform of the sequence floor((4 - sqrt(5))*n); complement of A187908.

%C See A187224. A187232(n) = A187907(n) for n=1..20; A187232(21)=39 and A187907(21)=40.

%t r=4-5^(1/2);

%t seqA = Table[Floor[r*n], {n, 1, 220}] (* A187330 *)

%t seqB = Table[n, {n, 1, 220}]; (* A000027 *)

%t jointRank[{seqA_,

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

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

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

%t limseqU =

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

%t jointRank[{seqA, seqB}]][[1]] (* A187907 *)

%t Complement[Range[Length[seqA]], limseqU] (* A187908 *)

%t (* _Peter J. C. Moses_, Mar 15 2011 *)

%o (Maxima) makelist(floor((4-sqrt(5))*n),n,1,100); /* _Martin Ettl_, Oct 17 2012 */

%Y Cf. A187224, A187908.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 15 2011