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.

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

1,3

Comments

See A360599 for the corresponding ratios.

Links

Table of n, a(n) for n=1..66.

Example

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

Prog

(PARI) See Links section.
(Python)
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

Crossrefs

Cf. A084337, A360599.

Sequence in context: A372261 A220794 A220959 * A243434 A265416 A199953

Adjacent sequences: A360595 A360596 A360597 * A360599 A360600 A360601

Keyword

nonn

Author

Rémy Sigrist, Feb 13 2023

Status

approved