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Search: id:A140129
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| A140129 |
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a(n) = numerator of c(n) = if n=1 then 0 else if n < 3*2^[Log2(n)-1] then (c([n/2])+c([(n+1)/2]))/2 else c(n-2^[Log2(n)])+1;. |
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+0
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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COMMENT
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C(k) = {a(n)/A140130(n): 2^(k-1) <= n < 2^k} = nonnegative Conway
numbers created on day k according 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;
for n>1: a(A023758(n))=A002262(n-2) and A140130(A023758(n))=1;
a(n)=a(n-2^[Log2(n))+A140130(n-2^[Log2(n)) for n with
3*2^[Log2(n)-1]<=n<2^[Log2(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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R. Zumkeller, Table of n, a(n) for n = 1..8191
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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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Cf. A000523, A007283.
Sequence in context: A079603 A055186 A124035 this_sequence A029347 A058725 A068446
Adjacent sequences: A140126 A140127 A140128 this_sequence A140130 A140131 A140132
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KEYWORD
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nonn,frac
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2008
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