A166006 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.
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, 1, 0, -1, -2, -1, -2, -3, -4, -5, -4, -5, -4, -3, -4, -3, -4, -5, -6, -5, -4, -5, -6, -7, -8, -7, -8, -9, -10, -9, -8, -9, -8, -9, -10, -9, -8, -9, -10, -11, -10, -11, -12, -11, -10, -11
Offset: 1
Examples
The first five digits of the expansion are 1, 1, 0, 0, 1. Starting at 0, we get 0 + 1 + 1 - 1 - 1 + 1 = 1, so a(5) = 1.
Links
- Hans Havermann, Table of n, a(n) for n = 1..10000
- Hans Havermann, A walk in base-two pi
Crossrefs
Formula
a(n) = Sum_{k=1..n} (2*b(k) - 1), where b(n) is the n-th binary digit of Pi.
Comments