A065675 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, ...].

-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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 22 2001

Keywords

• sign

Comments

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

Links

• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A065674, A065676, A065658.

Programs

Maple

[seq(exp_of_2(SternBrocot0_1frac(j)),j=1..128)];
SternBrocot0_1frac := proc(n) local m; m := n + 2^floor_log_2(n); SternBrocotTreeNum(m)/SternBrocotTreeDen(m); end;
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;