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%I A140129 #23 Jun 23 2021 12:32:32
%S A140129 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,
%T A140129 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,
%U A140129 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
%N A140129 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)).
%C A140129 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 A140129 c(2^n-1) = n-1; c(2^n) = 0; c(3*2^n) = 1; c(5*2^n) = 1/2;
%C A140129 for n>1: a(A023758(n)) = A002262(n-2) and A140130(A023758(n))=1;
%C A140129 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)).
%D A140129 D. E. Knuth, Surreal Numbers, Addison-Wesley, Reading, 1974.
%H A140129 Reinhard Zumkeller, <a href="/A140129/b140129.txt">Table of n, a(n) for n = 1..8191</a>
%H A140129 Wikipedia, <a href="http://en.wikipedia.org/wiki/Surreal_number">Surreal number</a>
%e A140129 C(1) = {0};
%e A140129 C(2) = {0, 1};
%e A140129 C(3) = {0, 1/2, 1,2};
%e A140129 C(4) = {0, 1/4, 1/2, 3/4, 1, 3/2, 2, 3};
%e A140129 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}.
%Y A140129 Cf. A000523, A007283.
%K A140129 nonn,frac,look
%O A140129 1,7
%A A140129 _Reinhard Zumkeller_, May 14 2008

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