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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.

%I A360598 #8 Feb 14 2023 12:54:57
%S A360598 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,
%T A360598 19,399,1,22,506,1,24,600,1,26,702,1,28,812,1,30,930,1,32,1056,1,34,
%U A360598 1190,1,36,1332,1,38,1482,1,40,1640,1,42,1806,1,44,1980,1,46
%N 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.
%C A360598 See A360599 for the corresponding ratios.
%e A360598 The first terms, alongside the corresponding ratios, are:
%e A360598   n   a(n)  Ratio between a(n) and a(n+1)
%e A360598   --  ----  -----------------------------
%e A360598    1     1       1
%e A360598    2     1       2
%e A360598    3     2       3
%e A360598    4     6       6
%e A360598    5     1       4
%e A360598    6     4       5
%e A360598    7    20      20
%e A360598    8     1       7
%e A360598    9     7       8
%e A360598   10    56      56
%e A360598   11     1       9
%e A360598   12     9      10
%o A360598 (PARI) See Links section.
%o A360598 (Python)
%o A360598 from itertools import islice
%o A360598 def agen(): # generator of terms
%o A360598     an, ratios = 1, set()
%o A360598     while True:
%o A360598         yield an
%o A360598         k = 1
%o A360598         q, r = divmod(max(k, an), min(k, an))
%o A360598         while r != 0 or q in ratios:
%o A360598             k += 1
%o A360598             q, r = divmod(max(k, an), min(k, an))
%o A360598         an = k
%o A360598         ratios.add(q)
%o A360598 print(list(islice(agen(), 66))) # _Michael S. Branicky_, Feb 13 2023
%Y A360598 Cf. A084337, A360599.
%K A360598 nonn
%O A360598 1,3
%A A360598 _Rémy Sigrist_, Feb 13 2023