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A327119 Sequence obtained by swapping each (k*(2n))-th element of the nonnegative integers with the (k*(2n+1))-th element, for all k>0 in ascending order, omitting the first term. 3
0, 1, 3, 2, 7, 4, 8, 6, 14, 5, 15, 10, 20, 12, 17, 9, 34, 16, 27, 18, 31, 13, 29, 22, 47, 19, 39, 11, 48, 28, 44, 30, 76, 21, 51, 26, 62, 36, 53, 25, 69, 40, 55, 42, 75, 24, 65, 46, 97, 35, 63, 33, 94, 52, 71, 43, 95, 37, 87, 58, 90, 60, 89, 32, 167, 50, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The first term must be omitted because it does not converge.

Start with the sequence of nonnegative integers [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...].

Swap all pairs specified by k=1, resulting in [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, ...], so the first term of the final sequence is 0 (No swaps for k>1 will affect this term).

Swap all pairs specified by k=2, resulting in [3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, ...], so the second term of the final sequence is 1 (No swaps for k>2 will affect this term).

Swap all pairs specified by k=3, resulting in [2, 0, 1, 3, 7, 4, 8, 6, 11, 5, 9, ...], so the third term of the final sequence is 3 (No swaps for k>3 will affect this term).

Continue for all values of k.

a(n) is equivalent to -A327093(-n), if A327093 is extended to all integers.

It appears that n is an odd prime number iff a(n+1)=n-1. If true, is there a formal analogy with the Sieve of Eratosthenes (by swapping instead of marking terms), or is this another type of sieve? - Jon Maiga, May 31 2021

LINKS

Jennifer Buckley, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A004442(A327420(n)) (conjectured). - Jon Maiga, May 31 2021

PROG

(golang) func a(n int) int {

    for k := n; k > 0; k-- {

        if n%k == 0 {

            if (n/k)%2 == 0 {

                n = n + k

            } else {

                n = n - k

            }

        }

    }

    return n

}

CROSSREFS

Cf. A004442, A327093, A327420.

Inverse: A327120.

Sequence in context: A182651 A175055 A085168 * A113658 A318462 A273926

Adjacent sequences:  A327116 A327117 A327118 * A327120 A327121 A327122

KEYWORD

nonn

AUTHOR

Jennifer Buckley, Sep 13 2019

STATUS

approved

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)