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A075075
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a(1) = 1, a(2) = 2 and then the smallest number not occurring earlier such that every term divides the product of its neighbors: a(n-1)*a(n+1)/a(n) is an integer.
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5
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1, 2, 4, 6, 3, 5, 10, 8, 12, 9, 15, 20, 16, 24, 18, 21, 7, 11, 22, 14, 28, 26, 13, 17, 34, 30, 45, 27, 33, 44, 32, 40, 25, 35, 42, 36, 48, 52, 39, 51, 68, 56, 70, 50, 55, 66, 54, 63, 49, 77, 88, 64, 72, 81, 90, 60, 38, 19, 23, 46, 58, 29, 31, 62, 74, 37, 41, 82, 76, 114, 57, 43
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OFFSET
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1,2
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COMMENTS
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This is a permutation of natural numbers. [Leroy Quet asks if this is a theorem or just a conjecture? May 06 2009]
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10000
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MAPLE
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b:= proc(n) option remember; false end: a:= proc(n) option remember; local k, m; if n<3 then b(n):= true; n else m:= denom (a(n-2) /a(n-1)); for k from m by m while b(k) do od; b(k):= true; k fi end: seq (a(n), n=1..100); [From Alois P. Heinz, May 16 2009]
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MATHEMATICA
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f[s_List] := Block[{m = Numerator[ s[[ -1]]/s[[ -2]] ]}, k = m; While[ MemberQ[s, k], k += m]; Append[s, k]]; Nest[f, {1, 2}, 70] [From Robert G. Wilson v, May 20 2009]
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PROG
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(Haskell)
import Data.List (delete)
a075075 n = a075075_list !! (n-1)
a075075_list = 1 : 2 : f 1 2 [3..] where
f z z' xs = g xs where g (u:us) =
if (z * u) `mod` z' > 0 then g us else u : f z' u (delete u xs)
-- Reinhard Zumkeller, Dec 19 2012
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CROSSREFS
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Cf. A075076 (ratios), A160256, A064413 (EKG sequence).
Cf. A160516 (inverse), A185635 (fixed points).
Sequence in context: A076179 A175213 A104492 * A088178 A161184 A140645
Adjacent sequences: A075072 A075073 A075074 * A075076 A075077 A075078
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KEYWORD
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nice,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 09 2002
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EXTENSIONS
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More terms from Sascha Kurz, Feb 03 2003
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STATUS
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approved
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