

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(n2^[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^(k1) <= n < 2^k} = nonnegative Conway numbers created on day k according to the genesis reported by Knuth.
c(2^n1) = n1; c(2^n) = 0; c(3*2^n) = 1; c(5*2^n) = 1/2;
for n>1: a(A023758(n)) = A002262(n2) and A140130(A023758(n))=1;
a(n) = a(n2^[Log2(n))+A140130(n2^[Log2(n)) for n with 3*2^[Log2(n)1]<=n<2^[Log2(n)].


REFERENCES

D. E. Knuth, Surreal Numbers, AddisonWesley, 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



