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1, 2, 3, 6, 4, 5, 20, 7, 8, 56, 9, 10, 90, 11, 12, 132, 13, 14, 182, 15, 16, 240, 17, 18, 306, 19, 21, 399, 22, 23, 506, 24, 25, 600, 26, 27, 702, 28, 29, 812, 30, 31, 930, 32, 33, 1056, 34, 35, 1190, 36, 37, 1332, 38, 39, 1482, 40, 41, 1640, 42, 43, 1806, 44
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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This sequence is a permutation of the positive integers with inverse A360600:
- we already know that all terms are distinct, so we just have to show that all integers appear,
- by contradiction: let r be the least value missing from this sequence,
- once the values 1..r-1 have appeared in this sequence, the sequence A360598 can only decrease finitely many times,
- the next increase in A360598 will correspond to the ratio r.
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LINKS
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EXAMPLE
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For n = 15:
so a(15) = 132 / 11 = 12.
For n = 16:
so a(16) = 132 / 1 = 132.
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PROG
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(PARI) See Links section.
(Python)
from itertools import islice
def agen(): # generator of terms
an, ratios = 1, set()
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)
yield q
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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