A330306 a(n) = floor(1/2 + {Pi^n}), where { } denotes fractional part.

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

Offset

1

Comments

Is there a 1-to-1 correspondence between real numbers r > 1 and their binary spectra defined as {floor (1/2 + r^n mod 1): n >= 1}? If so, can we recover the real number from its spectrum?

Links

Table of n, a(n) for n=1..87.

Mathematica

Array[Floor[1/2 + FractionalPart[Pi^#]] &, 105] (* Michael De Vlieger, Jan 25 2020 *)

Prog

(PARI) default(realprecision, 1000); a(n) = floor(frac(Pi^n) + 1/2); \\ Jinyuan Wang, Dec 14 2019

Crossrefs

Cf. A000796.

Sequence in context: A369658 A025464 A162518 * A300477 A355202 A353556

Adjacent sequences: A330303 A330304 A330305 * A330307 A330308 A330309

Keyword

nonn

Author

Daniel Forgues, Dec 13 2019

Extensions

More terms from Frank Ellermann, Feb 27 2020

Status

approved