A036414 Number of empty intervals when fractional_part(i*phi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 2, 0, 2, 3, 1, 2, 0, 3, 2, 4, 3, 1, 3, 3, 4, 3, 2, 4, 5, 0, 4, 5, 4, 8, 6, 6, 5, 2, 5, 5, 5, 5, 8, 5, 5, 4, 8, 6, 6, 5, 0, 6, 7, 8, 7, 6, 8, 8, 11, 9, 8, 10, 9, 4, 9, 9, 9, 8, 8, 9, 8, 12, 8, 8, 10, 9, 6, 9, 8, 11, 10, 8, 10, 10, 0, 10, 11, 9, 12, 12, 14

Offset

1,9

References

H. Steinhaus, Mathematical Snapshots, 3rd American ed. New York: Oxford University Press, pp. 48-49, 1983.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Equidistributed Sequence

Eric Weisstein's World of Mathematics, Golden Ratio

Mathematica

Table[Length@Complement[Range[n] - 1, Floor[n*FractionalPart[GoldenRatio*Range[n]]]], {n, 95}] (* Ivan Neretin, Jan 23 2018 *)
Table[Count[BinCounts[FractionalPart[GoldenRatio Range[n]], {0, 1, 1/n}], 0], {n, 95}] (* Eric W. Weisstein, Apr 17 2024 *)

Crossrefs

Cf. A036415 (positions of 0).

Cf. similar sequences with other constants: A036412 (e), A036416 (Pi), A046157 (gamma).

Sequence in context: A029407 A259285 A099544 * A234954 A321201 A180649

Adjacent sequences: A036411 A036412 A036413 * A036415 A036416 A036417

Keyword

nonn,look

Author

Eric W. Weisstein

Status

approved