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%I #9 Mar 25 2019 06:29:58
%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 5) # 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
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