

A307048


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


7



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
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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 onetoone 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



