

A161924


Permutation of natural numbers: sequence A126441 without zeros.


15



1, 2, 3, 4, 5, 7, 8, 9, 6, 11, 15, 16, 17, 10, 19, 13, 23, 31, 32, 33, 18, 35, 12, 21, 14, 39, 27, 47, 63, 64, 65, 34, 67, 20, 37, 22, 71, 25, 43, 29, 79, 55, 95, 127, 128, 129, 66, 131, 36, 69, 38, 135, 24, 41, 26, 75, 45, 30, 143, 51, 87, 59, 159, 111, 191, 255, 256
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OFFSET

1,2


COMMENTS

Values appear in the order determined by A004760(n+1)and A062383(n).
The graph of this sequence looks very elegant.


LINKS

A. Karttunen, Table of n, a(n) for n = 1..1596 (first 18 rows)
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

The table begins:
1.2.4..8.16.32.64.128.256.512.1024
..3.5..9.17.33.65.129.257.513.1025
.......6.10.18.34..66.130.258..514
....7.11.19.35.67.131.259.515.1027
............12.20..36..68.132..260
.........13.21.37..69.133.261..517
............14.22..38..70.134..262
......15.23.39.71.135.263.519.1031
...................24..40..72..136
...............25..41..73.137..265
...................26..42..74..138
............27.43..75.139.267..523
.......................28..44...76
...............29..45..77.141..269
...................30..46..78..142
.........31.47.79.143.271.527.1039
...........................48...80
.......................49..81..145
...........................50...82
...................51..83.147..275
This can be viewed as an irregular table, where row r (>= 1) has A000041(r) elements, that is, as 1; 2,3; 4,5,7; 8,9,6,11,15; 16,17,10,19,13,23,31; etc. A125106 illustrates how each number is mapped to a partition.


MATHEMATICA

columns = 9; row[n_] := n  2^Floor[Log2[n]]; col[0] = 0; col[n_] := If[EvenQ[n], col[n/2] + DigitCount[n/2, 2, 1], col[(n  1)/2] + 1]; Clear[T]; T[_, _] = 0; Do[T[row[k], col[k]] = k, {k, 1, 2^columns}]; Table[DeleteCases[Table[T[n  1, k], {n, 1, 2^(k  1)}], 0], {k, 1, columns}] // Flatten (* JeanFrançois Alcover, Sep 09 2017 *)


CROSSREFS

Inverse: A166276. a(n) = A126441(A166274(n)). See A161919 for the version with each row sorted into ascending order.
A161511(a(n)) = A036042(n).
Sequence in context: A228683 A133017 A290019 * A034153 A004725 A129487
Adjacent sequences: A161921 A161922 A161923 * A161925 A161926 A161927


KEYWORD

nonn,tabf,look


AUTHOR

Alford Arnold, Jun 23 2009


EXTENSIONS

Edited and extended by Antti Karttunen, Oct 12 2009


STATUS

approved



