A307048 Permutation of the positive integers derived from the terms of A322469 having the form 6*k - 2.

2, 1, 6, 5, 10, 4, 14, 7, 18, 13, 22, 8, 26, 3, 30, 21, 34, 12, 38, 9, 42, 29, 46, 16, 50, 23, 54, 37, 58, 20, 62, 19, 66, 45, 70, 24, 74, 17, 78, 53, 82, 28, 86, 39, 90, 61, 94, 32, 98, 15, 102, 69, 106, 36, 110, 25, 114, 77, 118, 40, 122, 55

Offset

1,1

Comments

The sequence is the flattened form of an irregular table U(i, j) similar to table T(i, j) in A322469. U(i, j) = k is defined only for the elements T(i, j) which have the form 6*k - 2, so the table is sparsely filled.

Like in A322469, the columns in table U contain arithmetic progressions.

a(n) is a permutation of the positive integers, since A322469 is one, and since there is a one-to-one mapping between any a(n) = k and some A322469(m) = 6*k - 2.

There is a hierarchy of such permutations of the positive integers derived by mapping the terms of the form 6*k - 2 to k:

Level 1: A322469

Level 2: A307048 (this sequence)

Level 3: A160016 = 2, 1, 4, 6, 8, 3, ... period of (3 even, 1 odd number)

Level 4: A000027 = 1, 2, 3, 4 ... (the positive integers)

Level 5: A000027

Links

Table of n, a(n) for n=1..62.

Example

Table U(i, j) begins:
   i\j   1  2  3  4  5  6  7
   -------------------------
   1:
   4:          2
   7:                   1
  10:
  13:          6
  16:                5
  19:
  22:         10
  25:             4
  28:
  31:         14
-----
T(4, 3) = 10 = 6*2 - 2, therefore U(4, 3) = 2.
T(7, 6) =  4 = 6*1 - 2, therefore U(7, 6) = 1.

Prog

(Perl 5) # derived from A322469
  use integer; my $n = 1; my $i = 1; my $an;
  while ($i <= 1000) { # next row
    $an = 4 * $i - 1; &term();
    while ($an % 3 == 0) {
      $an /= 3; &term();
      $an *= 2; &term();
    } # while divisible by 3
    $i ++;
  } # while next row
  sub term {
    if (($an + 2) % 6 == 0) {
      my $bn = ($an + 2) / 6;
      print "$n $bn\n"; $n ++;
    }
  }

Crossrefs

Cf. A000027, A160016, A322469.

Sequence in context: A308431 A292667 A030770 * A188652 A333958 A114852

Adjacent sequences: A307045 A307046 A307047 * A307049 A307050 A307051

Keyword

nonn,easy

Author

Georg Fischer, Mar 21 2019

Status

approved