A116937 Expansion of Pi^2 in base 2.

1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,1

Comments

One expects Pi^2 to be equidistributed, base 2, with an equal asymptotic density of 0 and 1 in this sequence; equal density of 00, 01, 10, 11. The first 100 decimal places here have, as binary, a run of 7 0's and a run of 9 1's.

Links

Table of n, a(n) for n=1..105.

Formula

Pi^2 (base 2).

Example

1001.1101111 (base 2) ~ 9.8696 (base 10) ~ Pi^2. 100 decimal places precision here.
See also: A000796 Decimal expansion of Pi.
See also: A004601 Expansion of Pi in base 2.

Mathematica

RealDigits[Pi^2, 2, 100][[1]] (* Stefan Steinerberger, Mar 30 2006 *)

Crossrefs

Cf. A000796. Pi in various bases: A004601 to A004608, A000796, A068436 to A068440, A062964. Cf. A007514.

Sequence in context: A267292 A267178 A285277 * A267810 A267927 A030300

Adjacent sequences: A116934 A116935 A116936 * A116938 A116939 A116940

Keyword

base,cons,nonn

Author

Jonathan Vos Post, Mar 21 2006

Extensions

Mathematica program modified by Harvey P. Dale, Apr 02 2019

Status

approved