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