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A140129 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}. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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;

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)].

REFERENCES

D. E. Knuth, Surreal Numbers, Addison-Wesley, Reading, 1974.

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..8191

Wikipedia, Surreal number

EXAMPLE

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}.

CROSSREFS

Cf. A000523, A007283.

Sequence in context: A157897 A213910 A288002 * A029347 A303427 A176076

Adjacent sequences:  A140126 A140127 A140128 * A140130 A140131 A140132

KEYWORD

nonn,frac,look

AUTHOR

Reinhard Zumkeller, May 14 2008

STATUS

approved

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Last modified May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)