A187911 Rank transform of the sequence (1+floor(n*r)), where r=(-1+sqrt(5))/2; complement of A187912.

1, 3, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 31, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 47, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 63, 64, 66, 68, 69, 70, 71, 73, 74, 75, 77, 78, 80, 81, 82, 84, 86, 87, 89, 90, 91, 93, 94, 96, 98, 99, 100, 101, 103, 105, 106, 107, 108, 110, 111, 112, 114, 116, 117, 118, 119

Offset: 1

Author

Clark Kimberling, Mar 15 2011

Keywords

• nonn

Comments

See A187224.

Crossrefs

Cf. A187224, A187912.

Programs

Mathematica

r=(-1+5^(1/2))/2;
seqA = Table[1+Floor[r*n], {n, 1, 220}] (* A019446 *)
seqB = Table[n, {n, 1, 220}];  (* A000027 *)
jointRank[{seqA_,
   seqB_}] := {Flatten@Position[#1, {_, 1}],
    Flatten@Position[#1, {_, 2}]} &[
  Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@ seqB}, 1]];
limseqU =
 FixedPoint[jointRank[{seqA, #1[[1]]}] &,
   jointRank[{seqA, seqB}]][[1]] (* A187911 *)
Complement[Range[Length[seqA]], limseqU]  (* A187912 *)
(* Peter J. C. Moses, Mar 15 2011 *)