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A124652
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a(1)=1. a(n) = smallest positive integer not occurring earlier in the sequence such that every positive integer <= and coprime to (sum{k=1 to n-1} a(k)) is also coprime to a(n).
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0
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1, 2, 3, 4, 5, 9, 6, 8, 16, 12, 11, 7, 14, 28, 18, 24, 21, 27, 32, 31, 81, 10, 20, 13, 169, 22, 33, 19, 17, 39, 26, 49, 37, 44, 36, 48, 54, 64, 25, 35, 40, 29, 41, 15, 45, 30, 50, 80, 58, 52, 60, 72, 47, 1369, 42, 56, 98, 59, 57, 38, 76, 62, 116, 128, 75, 87, 23, 115, 46, 91
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Is this sequence a permutation of the positive integers?
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EXAMPLE
| The sum of the first 7 terms of the sequence is 30. The positive integers <= 30 and coprime to 30 are 1,7,11,13,17,19,23,29. The smallest positive integer not occurring among the first 7 terms of the sequence which is coprime to 1,7,11,13,17,19,23,29 is 8. (7 does not occur among the first 7 terms of {a(k)}, but 7 is not coprime to 7.) So a(8) = 8.
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MATHEMATICA
| f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[l_List] := Block[{k = 1, t = f[Plus @@ l]}, While[MemberQ[l, k] || Times @@ GCD[t, k] > 1, k++ ]; Append[l, k]]; Nest[g, {1}, 70] (*Chandler*)
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CROSSREFS
| Sequence in context: A095904 A096153 A083140 * A048623 A075161 A029636
Adjacent sequences: A124649 A124650 A124651 * A124653 A124654 A124655
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Dec 22 2006
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 24 2006
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