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A281426
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Numerator of n-th term of sequence (or tree) S of all rational numbers generated by these rules: 0 is in S; if x is in S then x + 1 is in S, and if x + 1 is nonzero, then -1/(x + 1) is in S; duplicates are deleted as they occur.
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1
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0, 1, -1, 2, -1, 3, -1, 1, -2, 4, -1, 2, -3, 3, -2, 5, -1, 3, -4, 5, -3, 5, -2, 1, -3, 6, -1, 4, -5, 7, -4, 8, -3, 2, -5, 7, -2, 3, -5, 4, -3, 7, -1, 5, -6, 9, -5, 11, -4, 3, -7, 11, -3, 5, -8, 7, -5, 9, -2, 5, -7, 8, -5, 7, -3, 1, -4, 8, -1, 6, -7, 11, -6, 14
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OFFSET
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1,4
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COMMENTS
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See A232890 for the corresponding denominators and additional comments.
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LINKS
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EXAMPLE
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To generate S, the number 0 begets (1,-1), whence 1 begets 2 and -1/2, whereas -1 begets 0 and -1/2, both of which are (deleted )duplicates, so that g(3) = (2, -1/2). The resulting concatenation of all the generations g(n) begins with 0, 1, -1, 2, -1/2, 3, -1/3, 1/2, -2, 4, -1/4, so that A232890 begins with 0, 1, -1, 2, -1, 3, -1, 1, -2, 4.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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frac,sign
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AUTHOR
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STATUS
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approved
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