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;
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)).
REFERENCES
D. E. Knuth, Surreal Numbers, Addison-Wesley, Reading, 1974.
LINKS
Reinhard 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
KEYWORD
AUTHOR
Reinhard Zumkeller, May 14 2008
STATUS
approved