A346969 1 together with the square array T(n,k) read by upward antidiagonals in which T(n, k), n >= 1, is the n-th odd number j >= 3 such that the symmetric representation of sigma of j has k >= 2 parts.

1, 3, 5, 9, 7, 15, 21, 11, 25, 27, 63, 13, 35, 33, 81, 147, 17, 45, 39, 99, 171, 357, 19, 49, 51, 117, 189, 399, 903, 23, 77, 55, 153, 207, 441, 987, 2499, 29, 91, 57, 165, 243, 483, 1029, 2709, 6069, 31, 121, 65, 195, 261, 513, 1113, 2793, 6321, 13915, 37, 135, 69, 231, 275, 567, 1197, 2961, 6325, 14847, 29095

Offset

1,2

Comments

This sequence is a permutation of the odd positive integers.

The first row of table T(n,k) preceded by a(1) = 1 is A239663; the first column is the sequence A065091 of odd primes; the second column contains the squares of the odd primes as a subsequence (see also A247687).

Links

Table of n, a(n) for n=1..67.

Example

The 10x10 initial submatrix of table T(n,k):
n\k | 2   3    4    5     6     7     8      9      10     11  ...
------------------------------------------------------------------
  1 | 3   9    21   63    147   357   903    2499   6069   13915
  2 | 5   15   27   81    171   399   987    2709   6321   14847
  3 | 7   25   33   99    189   441   1029   2793   6325   15125
  4 | 11  35   39   117   207   483   1113   2961   6783   15141
  5 | 13  45   51   153   243   513   1197   3025   6875   15351
  6 | 17  49   55   165   261   567   1239   3087   6909   15729
  7 | 19  77   57   195   275   609   1265   3249   7011   16023
  8 | 23  91   65   231   279   621   1281   3339   7203   16611
  9 | 29  121  69   255   297   651   1375   3381   7353   16779
  10| 31  135  75   273   333   729   1407   3591   7581   17157
   ...
a(9) = 25 = T(3,3) since only 9 and 15 are smaller odd numbers whose symmetric representation of sigma consists of three parts. All 3 parts of the symmetric representation of sigma for 9 and for 25 have width 1 while the center part for that of 15 has width 2.

Mathematica

(* function a341969 is defined in A341969 *)
sArray[b_, pMax_] := Module[{list=Table[{}, pMax+1], i, p}, For[i=3, i<=b, i+=2, p=Length[Select[SplitBy[a341969[i], #!=0&], #[[1]]!=0&]]; If[p<=pMax+1&&Length[list[[p]]]<pMax, AppendTo[list[[p]], i]]]; If[MatrixQ[Rest[list]], Transpose[Rest[list]], "square matrix not filled"]]
parts[n_] := n-row[n-1](row[n-1]+1)/2
rank[n_] := row[n-1]-parts[n]+2
a346969[sMatrix_, aD_] := Prepend[Map[sMatrix[[ rank[#], parts[#]]] &, Range[aD (aD + 1)/2]], 1] /; MatrixQ[sMatrix] && aD <= Length[sMatrix]
m40000=sArray[40000, 11] (* entire 11x11 table filled *)
a346969[m40000, 11] (* sequence data: 1 followed by the first 11 antidiagonals in the table *)

Crossrefs

Cf. A065091, A237270, A237271, A237593, A239663, A247687, A320537, A341969, A341970, A341971, A348171.

Sequence in context: A332818 A348437 A100463 * A166722 A094549 A029642

Adjacent sequences: A346966 A346967 A346968 * A346970 A346971 A346972

Keyword

nonn,tabf

Author

Hartmut F. W. Hoft, Oct 06 2021

Status

approved