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%I #19 Feb 05 2024 18:39:22
%S 1,2,1,0,1,0,-1,0,-1,-2,-3,-4,-3,-2,-1,0,1,2,1,2,3,2,3,2,3,2,3,2,1,0,
%T 1,0,-1,-2,-1,-2,-3,-4,-5,-4,-5,-4,-3,-4,-3,-4,-5,-6,-5,-4,-5,-6,-7,
%U -8,-7,-8,-9,-10,-9,-8,-9,-8,-9,-10,-9,-8,-9,-10,-11,-10,-11,-12,-11,-10,-11
%N Distance from the origin using the binary expansion of Pi to walk the number line: Start at the origin; subtract one for each '0' digit, and add one for each '1' digit.
%C Of the first 10^10 terms, 5738590822 are positive and 4261262135 are negative. - _Hans Havermann_, Nov 27 2016
%H Hans Havermann, <a href="/A166006/b166006.txt">Table of n, a(n) for n = 1..10000</a>
%H Hans Havermann, <a href="http://gladhoboexpress.blogspot.ca/2016/11/a-walk-in-base-two-pi.html">A walk in base-two pi</a>
%F a(n) = Sum_{k=1..n} (2*b(k) - 1), where b(n) is the n-th binary digit of Pi.
%e The first five digits of the expansion are 1, 1, 0, 0, 1.
%e Starting at 0, we get 0 + 1 + 1 - 1 - 1 + 1 = 1, so a(5) = 1.
%Y Cf. A004601, A039624 (indices of zero), A278737 (record maxima), A278738 (record minima), A369900.
%K base,look,sign
%O 1,2
%A Steven Lubars (lubars(AT)gmail.com), Oct 03 2009