A036416 Number of empty intervals when fractional_part(i*Pi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

0, 1, 1, 1, 1, 0, 0, 1, 2, 3, 4, 4, 5, 7, 7, 7, 8, 9, 10, 11, 14, 12, 12, 14, 13, 14, 16, 21, 15, 17, 18, 16, 18, 19, 21, 20, 20, 21, 20, 22, 22, 23, 21, 22, 22, 23, 24, 25, 27, 21, 24, 24, 23, 25, 25, 28, 22, 25, 24, 26, 25, 25, 27, 21, 25, 24, 26, 24, 25, 25, 21, 24, 22, 23, 22

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Equidistributed Sequence.

Crossrefs

Cf. A036417 (positions of 0).

Cf. similar sequences with other constants: A036412 (e), A036414 (phi), A046157 (gamma).

Programs

Mathematica

Table[Length@Complement[Range[n] - 1, Floor[n*FractionalPart[Pi*Range[n]]]], {n, 75}] (* Ivan Neretin, Jan 23 2018 *)