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

1,2

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.

Links

Table of n, a(n) for n=1..92.

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*)

Crossrefs

Cf. A187224, A187571, A045749, A045750.

Sequence in context: A171948 A287527 A045749 * A045671 A276341 A098572

Adjacent sequences: A187567 A187568 A187569 * A187571 A187572 A187573

Keyword

nonn

Author

Clark Kimberling, Mar 11 2011

Status

approved