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A361321
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Lexicographically earliest infinite sequence of distinct elements of A000469 such that, for n > 2, a(n) has a common factor with a(n-1) but not with a(n-2).
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9
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1, 6, 10, 35, 21, 33, 22, 14, 91, 39, 15, 55, 77, 42, 26, 65, 85, 34, 38, 57, 51, 119, 70, 30, 69, 161, 133, 95, 110, 46, 299, 143, 66, 58, 145, 105, 78, 62, 155, 115, 138, 74, 185, 165, 87, 203, 154, 82, 123, 93, 217, 182, 86, 129, 111, 259, 238, 94, 141, 159
(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 variant of A360519 where we only consider nonprime squarefree numbers (A000469).
Theorem: a(1) = 1, a(2) = 6; thereafter, a(n) is the smallest nonprime squarefree number m not yet in the sequence such that
(i) gcd(m, a(n-1)) > 1,
(ii) gcd(m, a(n-2)) = 1, and
(iii) m does not divide a(n-1).
Conjecture: The sequence is a permutation of A000469.
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LINKS
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Scott R. Shannon, Image of the first 500000 terms in color. The terms with a lowest prime factor of 2,3,5,7,9,11,13,17,19,>=23 are colored white, red, orange, yellow, green, blue, indigo, violet, gray respectively.
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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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