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A233696
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Positions of integers in the sequence (or tree) S generated in order by these rules: 0 is in S; if x is in S then x + 1 is in S; if nonzero x is in S then 1/x is in S; if x is in S, then i*x is in S; where duplicates are deleted as they occur.
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5
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1, 2, 3, 5, 10, 11, 18, 23, 30, 49, 56, 102, 109, 212, 219, 443, 450, 926, 933, 1939, 1946, 4064, 4071, 8509, 8516, 17816, 17823, 37303, 37310, 78105, 78112, 163544, 163551
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OFFSET
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1,2
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COMMENTS
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It can be proved using the division algorithm for Gaussian integers that S is the set of Gaussian rational numbers: (b + c*i)/d, where b,c,d are integers and d is not 0.
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LINKS
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EXAMPLE
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The first 16 numbers generated are as follows: 0, 1, 2, i, 3, 1/2, 2 i, 1 + i, -i, -1, 4, 1/3, 3 i, 3/2, i/2, 1 + 2 i. Positions of integers 0, 1, 2, 3, -1, 4,... are 1,2,3,5,10,11,....
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MATHEMATICA
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Off[Power::infy]; x = {0}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, x + 1, 1/x, I*x} /. ComplexInfinity -> 0]]], {18}]; On[Power::infy]; t1 = Flatten[Position[x, _?(IntegerQ[#] && NonNegative[#] &)]] (*A233694*)
t2 = Flatten[Position[x, _?(IntegerQ[#] && Negative[#] &)]] (*A233695*)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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Definition and example corrected. - R. J. Mathar, May 06 2017
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STATUS
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approved
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