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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

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OFFSET

1,2

COMMENTS

Of the first 10^10 terms, 5738590822 are positive and 4261262135 are negative. - Hans Havermann, Nov 27 2016

LINKS

Hans Havermann, Table of n, a(n) for n = 1..10000

Hans Havermann, A walk in base-two pi

FORMULA

a(n) = Sum_{k=1..n} (2*b(k) - 1), where b(n) is the n-th binary digit of Pi.

EXAMPLE

The first five digits of the expansion are 1, 1, 0, 0, 1.