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A097465
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a(1) = 1; for n>1, a(n) = smallest positive integer which is not among earlier terms of sequence, is coprime to a(n-1) and is not equal to a(n-1) +- 1.
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1
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1, 3, 5, 2, 7, 4, 9, 11, 6, 13, 8, 15, 17, 10, 19, 12, 23, 14, 25, 16, 21, 26, 29, 18, 31, 20, 27, 22, 35, 24, 37, 28, 33, 38, 41, 30, 43, 32, 39, 34, 45, 47, 36, 49, 40, 51, 44, 53, 42, 55, 46, 57, 50, 59, 48, 61, 52, 63, 58, 65, 54, 67, 56, 69, 62, 71, 60, 73, 64, 75, 68, 77
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OFFSET
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1,2
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COMMENTS
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A permutation of the positive integers.
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LINKS
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Table of n, a(n) for n=1..72.
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EXAMPLE
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a(8) = 11 because, among the positive integers not occurring earlier in the sequence (6,8,10,11,12,...), 11 is the smallest which is coprime to a(7)=9, is not a(7)+1=10 and is not a(7)-1=8.
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MAPLE
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A:=proc(n) option remember; local t, S; S:=({$1..1000} minus {seq(A(i), i=1..n-1)}) minus {A(n-1)-1, A(n-1)+1}; t:=min(S[]); while igcd(A(n-1), t)>1 do S:=S minus {t}; t:=min(S[]) od; t end: A(1):=1: seq(A(n), n=1..200); (Mihailovs)
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = Block[{t = Table[ a[i], {i, n - 1}], k = 2}, While[k == a[n - 1] - 1 || k == a[n - 1] + 1 || GCD[a[n - 1], k] != 1 || Position[t, k] != {}, k++ ]; k]; Table[ a[n], {n, 50}] (from Robert G. Wilson v Aug 23 2004)
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CROSSREFS
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Cf. A093714, A097467.
Sequence in context: A164611 A182813 A073897 * A120683 A210042 A079313
Adjacent sequences: A097462 A097463 A097464 * A097466 A097467 A097468
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Aug 23 2004
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EXTENSIONS
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More terms from Alec Mihailovs (alec(AT)mihailovs.com) and Robert G. Wilson v, Aug 23 2004
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STATUS
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approved
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