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A257218
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Lexicographically earliest sequence of distinct positive integers such that gcd(a(n), a(n-1)) takes no value more than twice.
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7
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1, 2, 3, 6, 4, 8, 10, 5, 15, 9, 18, 12, 16, 24, 30, 20, 40, 32, 48, 36, 27, 54, 72, 60, 45, 75, 25, 50, 70, 7, 14, 28, 42, 21, 63, 126, 84, 56, 112, 64, 96, 120, 80, 100, 150, 90, 108, 81, 162, 216, 144, 168, 140, 35, 105, 210, 180, 135, 225, 300
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OFFSET
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1,2
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COMMENTS
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Presumably a(n) is a permutation of the positive integers.
Primes seem to occur in their natural order. 31 appears as a(7060). Primes p >= 37 are not found among the first 10000 terms.
Numbers n such that a(n)=n are 1, 2, 3, 12, 306, ...
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LINKS
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EXAMPLE
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After a(9)=15, the values 1, 2, 3, 4, 6, and 8 are already used, while 7 is forbidden because gcd(15,7)=1 and that value of GCD has already occurred twice, at (1,2) and (2,3). The minimal value which is neither used not forbidden is 9, so a(10)=9.
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MATHEMATICA
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a={1}; used=Array[0&, 10000]; Do[i=1; While[MemberQ[a, i] || used[[l=GCD[a[[-1]], i]]]>=2, i++]; used[[l]]++; AppendTo[a, i], {n, 2, 100}]; a (* Ivan Neretin, Apr 18 2015 *)
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PROG
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(Haskell)
import Data.List (delete); import Data.List.Ordered (member)
a257218 n = a257218_list !! (n-1)
a257218_list = 1 : f 1 [2..] a004526_list where
f x zs cds = g zs where
g (y:ys) | cd `member` cds = y : f y (delete y zs) (delete cd cds)
| otherwise = g ys
where cd = gcd x y
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CROSSREFS
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Other minimal sequences of distinct positive integers that match some condition imposed on a(n) and a(n-1):
A081145 (absolute differences are unique),
A163252 (differ by one bit in binary),
A077220 (sum is a triangular number),
A073666 (product plus 1 is a prime),
A081943 (product minus 1 is a prime),
A091569 (product plus 1 is a square),
A100208 (sum of squares is a prime).
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KEYWORD
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AUTHOR
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STATUS
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approved
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