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A085084
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Smallest number not yet used which is not a prime but is relatively prime to the previous term.
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4
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1, 4, 9, 8, 15, 14, 25, 6, 35, 12, 49, 10, 21, 16, 27, 20, 33, 26, 45, 22, 39, 28, 51, 32, 55, 18, 65, 24, 77, 30, 91, 34, 57, 40, 63, 38, 69, 44, 75, 46, 81, 50, 87, 52, 85, 36, 95, 42, 115, 48, 119, 54, 121, 56, 93, 58, 99, 62, 105, 64, 111, 68, 117, 70, 123, 74, 125, 66
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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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Every composite number appears in this sequence. Eventually, every p^2 (p prime) will appear; if the smallest unused composite does not follow, it will appear no later than following the next p^2.
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LINKS
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MAPLE
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# Corrected Maple program from Chen Zekai, Mar 23 2015, added by N. J. A. Sloane, Mar 23 2015
A085084 := proc (q) local a, b, i, n; if q = 1 then print(1); return; elif q = 2 then print(1); print(4); return; fi; a := {1, 4}; b := 4; i := 2; print(1); print(4); while i < q do for n from 6 to q^2 doif not isprime(n) and gcd(b, n) = 1 and {} = a intersect {n} thenb := n; a := a union {n}; i := i+1; print(n); break; fi; od; od; end:A085084(10000):
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MATHEMATICA
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A085084 = {a[1]=1, a[2]=4}; a[n_] := a[n] = Catch[For[k = 6, True, k++, If[!PrimeQ[k] && !MemberQ[A085084, k] && CoprimeQ[a[n-1], k], AppendTo[A085084, k]; Throw[k]]]]; Table[ a[n], {n, 1, 68}] (* Jean-François Alcover, Jul 17 2012 *)
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PROG
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(Haskell)
import Data.List (find, delete)
import Data.Maybe (fromJust)
a085084 n = a085084_list !! (n-1)
a085084_list = 1 : f 1 a002808_list where
f x cs = y : f y (delete y cs) where
y = fromJust $ find ((== 1) . (gcd x)) cs
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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