A187570 Rank transform of the sequence ceiling(n/3); complement of A187571.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 90, 92, 93, 94, 96, 97, 98, 100, 101, 102, 103, 104, 105, 107, 108, 109, 111, 112, 113, 115, 116

Offset: 1

Author

Clark Kimberling, Mar 11 2011

Keywords

• nonn

Comments

Appears to be a duplicate of A045749. - R. J. Mathar, Mar 15 2011

The Mathematica programs shown at A187570 and A045749 confirm equality of the first 500 terms. - Clark Kimberling, Apr 02 2011

The sequence of which A187570 is the rank transform is (1,1,1,2,2,2,3,3,3,4,4,4,...), which is (A002264 without the initial three zeros). For a discussion on rank transforms, see A187224.

Crossrefs

Cf. A187224, A187571, A045749, A045750.

Programs

Mathematica

seqA = Table[Ceiling[n/3], {n, 1, 220}]  (*A002264*)
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]] (*A187570*)
Complement[Range[Length[seqA]], limseqU]  (*A187571*)
(*by Peter J. C. Moses, Mar 11 2011*)