A302342 Cumulative sums of the bits in the binary representation of Pi.

1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 19, 20, 20, 21, 21, 21, 21, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 27, 28, 29, 29, 29, 29

Offset

-1,2

Comments

The leading binary bits of Pi are 11.0010010000111111011010101000100010000101101000110000100011010011000...

Links

Table of n, a(n) for n=-1..67.

Formula

a(n) = sum of the bits with value 2^(-n) or larger.

a(n) = (A166006(n+2) + n + 2)/2. - Pontus von Brömssen, Nov 26 2020

Crossrefs

Partial sums of A004601.

A256108 is the sequence of -1 followed by those values of n for which a(n) is strictly greater than a(n-1).

Cf. A166006.

Sequence in context: A172471 A046155 A026819 * A137214 A284726 A319951

Adjacent sequences: A302339 A302340 A302341 * A302343 A302344 A302345

Keyword

nonn

Author

Lee A. Newberg, Apr 05 2018

Status

approved