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A217266 Take the natural numbers, then for each k: move the multiples of k to the right. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A056017 A091995 A066937 * A209637 A120750 A265672

Adjacent sequences:  A217263 A217264 A217265 * A217267 A217268 A217269

KEYWORD

nonn

AUTHOR

Paul Tek, Mar 17 2013

STATUS

approved

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Last modified April 17 14:32 EDT 2021. Contains 343063 sequences. (Running on oeis4.)