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 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. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 Jennifer Buckley, Table of n, a(n) for n = 1..10000 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 } (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 CROSSREFS For the sorted terms and the missing terms see A327445, A327446. Cf. A327119, A064494, A064627, A057032, A069829, A327420. Sequence in context: A057218 A087387 A275205 * A171039 A063904 A297929 Adjacent sequences:  A327090 A327091 A327092 * A327094 A327095 A327096 KEYWORD nonn AUTHOR Jennifer Buckley, Sep 13 2019 STATUS approved

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Last modified January 20 01:01 EST 2022. Contains 350467 sequences. (Running on oeis4.)