cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A327120 Inverse permutation to A327119.

Original entry on oeis.org

1, 2, 4, 3, 6, 10, 8, 5, 7, 16, 12, 28, 14, 22, 9, 11, 18, 15, 20, 26, 13, 34, 24, 82, 46, 40, 36, 19, 30, 23, 32, 21, 64, 52, 17, 50, 38, 58, 76, 27, 42, 244, 44, 56, 31, 70, 48, 25, 29, 100, 66, 35, 54, 39, 136, 43, 106, 88, 60, 118, 62, 94, 37, 51, 78, 47, 68, 86
Offset: 0

Views

Author

Jennifer Buckley, Sep 13 2019

Keywords

Links

Crossrefs

Inverse: A327119.

Programs

  • PARI
    a(n) = { my (d=0); while (n, d = select(t -> t>d, divisors(n))[1]; my (k=n/d); if (k%2, n-=d, n+=d)); return (d+1) } \\ Rémy Sigrist, Sep 14 2019

A327093 Sequence obtained by swapping each (k*(2n))-th element of the positive integers with the (k*(2n-1))-th element, for all k > 0, in ascending order.

Original entry on oeis.org

2, 3, 7, 5, 11, 13, 15, 10, 17, 19, 23, 25, 27, 21, 40, 16, 35, 36, 39, 37, 58, 33, 47, 50, 52, 43, 45, 34, 59, 78, 63, 31, 76, 55, 82, 67, 75, 57, 99, 56, 83, 112, 87, 61, 126, 69, 95, 92, 97, 96, 133, 71, 107, 81, 142, 79, 139, 91, 119, 155, 123, 93, 122, 51, 151, 146, 135
Offset: 1

Views

Author

Jennifer Buckley, Sep 13 2019

Keywords

Comments

Start with the sequence of positive integers [1, 2, 3, 4, 5, 6, 7, 8, ...].
Swap all pairs specified by k=1, that is, do the swaps (2,1),(4,3),(6,5),(8,7),..., resulting in [2, 1, 4, 3, 6, 5, 8, 7, ...], so the first term of the final sequence is 2 (No swaps for k>1 will affect this term).
Swap all pairs specified by k=2, that is, do the swaps (4,2),(8,6),(12,10),(16,14),..., resulting in [2, 3, 4, 1, 6, 7, 8, 5, ...], so the second term of the final sequence is 3 (No swaps for k>2 will affect this term).
Swap all pairs specified by k=3, that is, do the swaps (6,3),(12,9),(18,15),(24,21),... .
Continue for all values of k.
The complementary sequence 1, 4, 6, 8, 9, 12, 14, 18, 20, 22, 24, 26, 28, ... lists the numbers that never appear. Is there an alternative characterization of these numbers?
Equivalently, is there a characterization of the numbers (2, 3, 5, 7, 10, 11, 13, 15, 16, 17, 19, 21, 23, ...) that do appear? - N. J. A. Sloane, Sep 13 2019

Links

Crossrefs

For the sorted terms and the missing terms see A327445, A327446.
Cf. A327119, A064494, A064627, A057032, A069829, A327420.

Programs

  • Go
    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
}
  • SageMath
    def a(n):
    for k in srange(n, 0, -1):
        if k.divides(n):
            n += k if is_odd(n//k) else -k
    return n
print([a(n) for n in (1..67)]) # Peter Luschny, Sep 14 2019
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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