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%I #11 Jan 01 2024 13:19:53
%S 0,0,0,0,1,1,4,4,5,5,10,10,16,16,17,17,18,18,27,27,37,37,38,38,50,50,
%T 51,51,52,52,67,67,68,68,85,85,103,103,104,104,124,124,125,125,126,
%U 126,149,149,173,173,174,174,175,175,202,202,203,203,232,232,262,262,263,263
%N a(n)=sum(k=1,n, k mod sum(i=0,k-1,1-t(i))) where t(i)=A010060(i) is the Thue-Morse sequence.
%F Despite the definition, a(n) has an unexpectedly simple asymptotic behavior h: a(n)=(n/4)^2 +O(n) and more precisely it appears that : (n/4)^2-n/8 <= a(n) < (n/4)^2+n/2 with equality (on left side) for infinitely many values of n.
%o (PARI) a(n)=sum(k=1,n,k%sum(i=0,k-1,1-subst(Pol(binary(i)),x,1)%2))
%K nonn
%O 1,7
%A _Benoit Cloitre_, May 27 2003
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