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 A026367 a(n) = least k such that s(k) = n, where s = A026366. 4

%I

%S 1,2,4,5,7,8,9,10,12,13,15,16,17,18,20,21,23,24,26,27,29,30,31,32,34,

%T 35,37,38,39,40,42,43,45,46,48,49,51,52,53,54,56,57,59,60,61,62,64,65,

%U 67,68,69,70,72,73,75,76,77,78,80,81,83,84,86

%N a(n) = least k such that s(k) = n, where s = A026366.

%C Complement of A026328; also the rank transform (as at A187224) of A004526 (after removal of the initial two zeros). [From Clark Kimberling, Mar 10 2011]

%F a(n) = a(n-1)+2 if n is in the set 2A+1, a(n) = a(n-1)+1 if n is not in 2A+1 where 2A+1 = {2a(1)+1,2a(2)+1,2a(3)+1,...} = {3,5,9,11,15,17,19,21,25,27,31,33,...}. a(n) = (1+sqrt(3))/2*n+O(1) For example, a(3) = a(2)+2 = 2+2 = 4 since 3 is in 2A+1. a(10) = a(9)+1 = 12+1 = 13 since 10 is not in 2A+1. - _Benoit Cloitre_, Apr 23 2008

%t seqA = Table[Ceiling[n/2], {n, 1, 180}] (* A004526 *)

%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[{seqA, seqB}]][[1]] (* A026367 *)

%t Complement[Range[Length[seqA]], limseqU] (* A026368 *)

%t (* by Peter Moses, Mar 10 2011 *)

%Y Cf. A026368, A187224, A004526.

%K nonn

%O 1,2

%A _Clark Kimberling_

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