A360599 -id:A360599 - cp's OEIS frontend

A360600 Inverse permutation to A360599.

1, 2, 3, 5, 6, 4, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 7, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 10, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95

Offset: 1

Rémy Sigrist, Feb 13 2023

nonn

			A360599(59) = 42, so a(42) = 59.

Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A360599.

PARI
```
See Links section.
```

from itertools import islice
def agen(): # generator of terms
    an, ratios, inv, n = 1, set(), dict(), 1
    while True:
        k = 1
        q, r = divmod(max(k, an), min(k, an))
        while r != 0 or q in ratios:
            k += 1
            q, r = divmod(max(k, an), min(k, an))
        an = k
        ratios.add(q)
        inv[q] = len(ratios)
        while n in inv:
            yield inv[n]
            n += 1
print(list(islice(agen(), 67))) # Michael S. Branicky, Feb 13 2023

A360598 Lexicographically earliest sequence of positive integers such that the ratios between successive terms, { max(a(n), a(n+1)) / min(a(n), a(n+1)), n > 0 }, are distinct integers.

Original entry on oeis.org

1, 1, 2, 6, 1, 4, 20, 1, 7, 56, 1, 9, 90, 1, 11, 132, 1, 13, 182, 1, 15, 240, 1, 17, 306, 1, 19, 399, 1, 22, 506, 1, 24, 600, 1, 26, 702, 1, 28, 812, 1, 30, 930, 1, 32, 1056, 1, 34, 1190, 1, 36, 1332, 1, 38, 1482, 1, 40, 1640, 1, 42, 1806, 1, 44, 1980, 1, 46

Offset: 1

Rémy Sigrist, Feb 13 2023

nonn

See A360599 for the corresponding ratios.

			The first terms, alongside the corresponding ratios, are:
  n   a(n)  Ratio between a(n) and a(n+1)
  --  ----  -----------------------------
   1     1       1
   2     1       2
   3     2       3
   4     6       6
   5     1       4
   6     4       5
   7    20      20
   8     1       7
   9     7       8
  10    56      56
  11     1       9
  12     9      10

Cf. A084337, A360599.

PARI
```
See Links section.
```

from itertools import islice
def agen(): # generator of terms
    an, ratios = 1, set()
    while True:
        yield an
        k = 1
        q, r = divmod(max(k, an), min(k, an))
        while r != 0 or q in ratios:
            k += 1
            q, r = divmod(max(k, an), min(k, an))
        an = k
        ratios.add(q)
print(list(islice(agen(), 66))) # Michael S. Branicky, Feb 13 2023

cp's OEIS Frontend

A360600 Inverse permutation to A360599.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Python