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A161924 Permutation of natural numbers: sequence A126441 without zeros.

%I A161924 #11 Sep 09 2017 10:40:17
%S A161924 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,
%T A161924 27,47,63,64,65,34,67,20,37,22,71,25,43,29,79,55,95,127,128,129,66,
%U A161924 131,36,69,38,135,24,41,26,75,45,30,143,51,87,59,159,111,191,255,256
%N A161924 Permutation of natural numbers: sequence A126441 without zeros.
%C A161924 Values appear in the order determined by A004760(n+1)and A062383(n).
%C A161924 The graph of this sequence looks very elegant.
%H A161924 A. Karttunen, <a href="/A161924/b161924.txt">Table of n, a(n) for n = 1..1596 (first 18 rows)</a>
%H A161924 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A161924 The table begins:
%e A161924 1.2.4..8.16.32.64.128.256.512.1024
%e A161924 ..3.5..9.17.33.65.129.257.513.1025
%e A161924 .......6.10.18.34..66.130.258..514
%e A161924 ....7.11.19.35.67.131.259.515.1027
%e A161924 ............12.20..36..68.132..260
%e A161924 .........13.21.37..69.133.261..517
%e A161924 ............14.22..38..70.134..262
%e A161924 ......15.23.39.71.135.263.519.1031
%e A161924 ...................24..40..72..136
%e A161924 ...............25..41..73.137..265
%e A161924 ...................26..42..74..138
%e A161924 ............27.43..75.139.267..523
%e A161924 .......................28..44...76
%e A161924 ...............29..45..77.141..269
%e A161924 ...................30..46..78..142
%e A161924 .........31.47.79.143.271.527.1039
%e A161924 ...........................48...80
%e A161924 .......................49..81..145
%e A161924 ...........................50...82
%e A161924 ...................51..83.147..275
%e A161924 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.
%t A161924 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 (* _Jean-François Alcover_, Sep 09 2017 *)
%Y A161924 Inverse: A166276. a(n) = A126441(A166274(n)). See A161919 for the version with each row sorted into ascending order.
%Y A161924 A161511(a(n)) = A036042(n).
%K A161924 nonn,tabf,look
%O A161924 1,2
%A A161924 _Alford Arnold_, Jun 23 2009
%E A161924 Edited and extended by _Antti Karttunen_, Oct 12 2009