A307048 - OEIS

%I #12 Nov 13 2024 19:05:38

%S 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,

%T 54,37,58,20,62,19,66,45,70,24,74,17,78,53,82,28,86,39,90,61,94,32,98,

%U 15,102,69,106,36,110,25,114,77,118,40,122,55

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

%C 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.

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

%C 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.

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

%C   Level 1: A322469

%C   Level 2: A307048 (this sequence)

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

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

%C   Level 5: A000027

%e Table U(i, j) begins:

%e    i\j   1  2  3  4  5  6  7

%e    -------------------------

%e    1:

%e    4:          2

%e    7:                   1

%e   10:

%e   13:          6

%e   16:                5

%e   19:

%e   22:         10

%e   25:             4

%e   28:

%e   31:         14

%e -----

%e T(4, 3) = 10 = 6*2 - 2, therefore U(4, 3) = 2.

%e T(7, 6) =  4 = 6*1 - 2, therefore U(7, 6) = 1.

%o (Perl)

%o # Derived from A322469

%o use integer; my $n = 1; my $i = 1; my $an;

%o while ($i <= 1000) { # next row

%o   $an = 4 * $i - 1; &term();

%o   while ($an % 3 == 0) {

%o     $an /= 3; &term();

%o     $an *= 2; &term();

%o   } # while divisible by 3

%o   $i ++;

%o } # while next row

%o sub term {

%o   if (($an + 2) % 6 == 0) {

%o     my $bn = ($an + 2) / 6;

%o     print "$n $bn\n"; $n ++;

%o   }

%o }

%Y Cf. A000027, A160016, A322469.

%K nonn,easy

%O 1,1

%A _Georg Fischer_, Mar 21 2019