A187839 Rank transform of the sequence floor(n*sqrt(2)-1/2); complement of A187840.

1, 3, 4, 7, 8, 9, 12, 14, 15, 17, 19, 21, 22, 24, 26, 28, 30, 31, 33, 35, 37, 38, 41, 42, 44, 46, 47, 50, 51, 52, 55, 56, 58, 60, 62, 63, 65, 68, 69, 71, 73, 74, 76, 78, 80, 82, 83, 85, 86, 89, 90, 92, 94, 96, 98, 99, 101, 103, 104, 107, 108, 111, 112, 114, 116, 117, 119, 121, 123, 124, 126, 128, 130, 132, 134, 135, 137, 139, 140, 142, 144, 146

Offset: 1

Author

Clark Kimberling, Mar 13 2011

Keywords

• nonn

Comments

See A187224.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A187224, A187840.

Programs

Mathematica

r=2^(1/2);
seqA = Table[Floor[r*n-1/2], {n, 1, 220}]
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]] (* A187839 *)
Complement[Range[Length[seqA]], limseqU]  (* A187840 *)
(* Peter J. C. Moses, Mar 13 2011 *)