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A140129
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Let c(n) = 0 if n=1, (c(floor(n/2)) + c(floor((n+1)/2)))/2 if 1 < n < 3*2^floor(log_2(n)-1), and c(n-2^floor(log_2(n))) + 1 otherwise. Then a(n) = numerator(c(n)).
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4
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0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 3, 1, 3, 2, 3, 0, 1, 1, 3, 1, 5, 3, 7, 1, 5, 3, 7, 2, 5, 3, 4, 0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 9, 5, 11, 3, 13, 7, 15, 2, 9, 5, 11, 3, 7, 4, 5, 0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31
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OFFSET
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1,7
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COMMENTS
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C(k) = {a(n)/A140130(n): 2^(k-1) <= n < 2^k} = nonnegative Conway numbers created on day k according to the genesis reported by Knuth.
c(2^n-1) = n-1; c(2^n) = 0; c(3*2^n) = 1; c(5*2^n) = 1/2;
a(n) = a(n - 2^floor(log_2(n)) + A140130(n - 2^floor(log_2(n)) for n with 3*2^floor(log_2(n)-1) <= n < 2^floor(log_2(n)).
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REFERENCES
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D. E. Knuth, Surreal Numbers, Addison-Wesley, Reading, 1974.
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LINKS
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EXAMPLE
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C(1) = {0};
C(2) = {0, 1};
C(3) = {0, 1/2, 1,2};
C(4) = {0, 1/4, 1/2, 3/4, 1, 3/2, 2, 3};
C(5) = {0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1, 5/4, 3/2, 7/4, 2, 5/2, 3, 4}.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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