A065675 - OEIS

%I #5 May 01 2014 02:49:15

%S -1,0,1,-2,1,0,-2,0,1,-3,0,2,-3,0,2,-1,1,0,-1,2,0,-2,2,0,-2,3,0,-1,3,

%T 0,-1,0,1,-1,0,2,-1,0,2,-1,0,3,-1,0,3,-4,0,1,-4,0,1,-1,0,2,-1,0,2,-1,

%U 0,1,-1,0,1,-3,1,0,-4,2,0,-1,2,0,-1,3,0,-3,3,0,-4,1,0,-1,1,0,-1,2,0,-1,2,0,-1,1,0,-2,1,0,-2,1,0,-1,1,0,-1,1,0,-1,1,0

%N The exponent of 2 in the fractions of the range ]0,1[ Stern-Brocot tree (A007305/A007306) [1/2, 1/3, 2/3, 1/4, 2/5, 3/5, 3/4, 1/5, 2/7, 3/8, 3/7, 4/7, 5/8, 5/7, 4/5, ...].

%C The exponent is negative when the denominator (A007306) is even. These occur as every third term.

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%p [seq(exp_of_2(SternBrocot0_1frac(j)),j=1..128)];

%p SternBrocot0_1frac := proc(n) local m; m := n + 2^floor_log_2(n); SternBrocotTreeNum(m)/SternBrocotTreeDen(m); end;

%p exp_of_2 := proc(x) local f,m; f := ifactors(x)[2]; for m in f do if(2 = m[1]) then RETURN(m[2]); fi; od; RETURN(0); end;

%Y Cf. A065674, A065676, A065658.

%K sign

%O 1,4

%A _Antti Karttunen_, Nov 22 2001