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A355065
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Lexicographically earliest sequence of distinct positive integers such that if m and n are distinct and not coprime, then a(n) does not belong to the interval ceiling(a(m)/2)..2*a(m).
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2
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1, 2, 3, 5, 4, 11, 6, 23, 24, 47, 7, 95, 8, 191, 192, 383, 9, 767, 10, 1535, 1536, 3071, 12, 6143, 3072, 12287, 12288, 24575, 13, 49151, 14, 98303, 98304, 196607, 98305, 393215, 15, 786431, 786432, 1572863, 16, 3145727, 17, 6291455, 6291456, 12582911, 18
(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 nonnegative integers (when n is prime, a(n) is the least value not yet in the sequence).
The inverse sequence (A355066) has similarities with the Two-Up sequence (A090252) as A355066(n) is coprime to the next n terms (and to the floor(n/2) previous terms).
Note that the relation "u does not belong to the interval ceiling(v/2)..2*v" is symmetrical (for u, v > 0).
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LINKS
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EXAMPLE
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The first terms, alongside the forbidden values, are:
n a(n) Forbidden values
-- ---- ---------------------------------------------------
1 1 None
2 2 None
3 3 None
4 5 1..4 (from m=2)
5 4 None
6 11 1..4 (from m=2), 2..6 (from m=3), 3..10 (from m=4)
7 6 None
8 23 1..4 (from m=2), 3..10 (from m=4), 6..22 (from m=6)
9 24 2..6 (from m=3), 6..22 (from m=6)
10 47 1..4 (from m=2), 3..10 (from m=4), 2..8 (from m=5),
6..22 (from m=6), 12..46 (from m=8)
11 7 None
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PROG
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(PARI) See Links section.
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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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