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

Author

Rémy Sigrist, Feb 13 2023

Keywords

• nonn

Comments

See A360599 for the corresponding ratios.

Examples

			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
		

Crossrefs

Cf. A084337, A360599.

Programs

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