A217266 Take the natural numbers, then for each k: move the multiples of k to the right.

1, 2, 3, 4, 5, 7, 6, 8, 11, 13, 9, 10, 17, 12, 19, 14, 23, 16, 15, 25, 29, 31, 22, 26, 18, 21, 37, 20, 41, 34, 43, 32, 27, 28, 47, 35, 24, 38, 53, 30, 33, 59, 61, 46, 50, 39, 49, 67, 36, 44, 71, 58, 73, 55, 51, 79, 52, 62, 83, 40, 42, 89, 65, 74, 45, 97, 57, 101, 56, 82, 103, 68, 76, 64, 88, 107, 109, 86, 113, 48, 70, 69, 54, 75, 81, 94, 63, 77

Offset

1,2

Comments

This is a permutation of the natural numbers.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Example

Before step 3, the intermediate sequence is:
   1,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,21,20,23,22,...
We separate the multiples of 3 from the other numbers:
     3,        6,9,           12,15,            18,21,        ,...
   1,  2,5,4,7,    8,11,10,13,      14,17,16,19,      20,23,22,...
We move the multiples of 3 to the right:
               3,6,            9,12,            15,18,        ,...
   1,  2,5,4,7,    8,11,10,13,      14,17,16,19,      20,23,22,...
Thus, we obtain this intermediate sequence after step 3:
   1,2,5,4,7,3,6,8,11,10,13,9,12,14,17,16,19,15,18,20,23,22,...

Prog

(Perl)
my $max = 1000;
my @a = (1..$max);
sub move {
    my $k    = shift;
    my @res  = ();
    my @prev = ();
    foreach (@_) {
        if ($_ % $k==0) {
            push @res => @prev;
            @prev = ($_);
        } else {
            push @res => $_;
        }
    }
    return @res;
}
foreach my $k (2..$max) {
    @a = move($k => @a);
}
print join(", " => @a), "\n";

Crossrefs

Sequence in context: A338698 A361946 A066937 * A347539 A209637 A347540

Adjacent sequences: A217263 A217264 A217265 * A217267 A217268 A217269

Keyword

nonn

Author

Paul Tek, Mar 17 2013

Status

approved