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Search: id:A124653
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| A124653 |
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a(1)=1. a(2)=2. a(n) = smallest positive integer not occurring earlier in the sequence such that every positive integer <= and coprime to (a(n-1)+a(n-2)) is also coprime to a(n). |
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1
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| 1, 2, 3, 5, 4, 9, 13, 8, 7, 15, 11, 16, 27, 43, 10, 53, 21, 32, 59, 49, 6, 25, 31, 14, 45, 61, 64, 125, 63, 47, 20, 67, 29, 12, 41, 71, 28, 33, 73, 106, 179, 19, 18, 37, 55, 23, 24, 79, 103, 26, 81, 107, 94, 201, 295, 62, 17, 83, 40, 123, 163, 22, 185, 69, 127, 56, 183, 239
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Is this sequence a permutation of the positive integers?
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EXAMPLE
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a(6)+a(7) = 22. The positive integers <= 22 and coprime to 22 are 1,3,5,7,9,13,15, 17,19,21. The smallest positive integer not occurring among the first 7 terms of the sequence which is coprime to 1,3,5,7,9,13,15,17,19, 21 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
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f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[l_List] := Block[{k = 1, t = f[l[[ -1]] + l[[ -2]]]}, While[MemberQ[l, k] || Times @@ GCD[t, k] > 1, k++ ]; Append[l, k]]; Nest[g, {1, 2}, 66] (*Chandler*)
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CROSSREFS
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Sequence in context: A085875 A060030 A081025 this_sequence A085947 A069202 A100932
Adjacent sequences: A124650 A124651 A124652 this_sequence A124654 A124655 A124656
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Dec 22 2006
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 24 2006
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