A278737 -id:A278737 - cp's OEIS frontend

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

Steven Lubars (lubars(AT)gmail.com), Oct 03 2009

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

			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.

Hans Havermann, Table of n, a(n) for n = 1..10000
Hans Havermann, A walk in base-two pi

Cf. A004601, A039624 (indices of zero), A278737 (record maxima), A278738 (record minima), A369900.

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

A278738 a(n) is the index of the first occurrence of -n in A166006.

Original entry on oeis.org

7, 10, 11, 12, 39, 48, 53, 54, 57, 58, 69, 72, 77, 86, 91, 92, 101, 102, 103, 104, 115, 130, 135, 138, 139, 140, 141, 142, 145, 148, 155, 156, 159, 160, 163, 164, 169, 196, 197, 198, 201, 202, 203, 204, 273, 274, 275, 276, 279, 280, 281, 306, 307, 308, 309, 312, 1955

Offset: 1

Hans Havermann, Nov 27 2016

nonn

These are necessarily the indices of record minima in A166006.

			-3 first occurs in A166006 at position 11, so a(3) = 11.

Hans Havermann, Table of n, a(n) for n = 1..10000
Hans Havermann, Table of n, a(n) for n = 1..162168

Cf. A166006, A039624, A278737.

cp's OEIS Frontend

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.

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