A036414 -id:A036414 - cp's OEIS frontend

A046157 Number of empty intervals when fractional_part(i*gamma) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions, where gamma is the Euler-Mascheroni constant.

0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 3, 0, 3, 5, 3, 3, 3, 2, 0, 3, 2, 2, 2, 1, 1, 0, 2, 3, 4, 3, 3, 3, 7, 6, 7, 7, 8, 8, 13, 10, 10, 10, 12, 11, 6, 13, 14, 14, 14, 14, 15, 26, 16, 19, 14, 17, 18, 18, 19, 18, 20, 18, 21, 18, 20, 20, 21, 21, 19, 21, 15, 20, 23, 21, 21, 20, 22, 26, 21, 22, 20

Offset: 1

Eric W. Weisstein

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

Cf. A046158 (positions of 0).

Similar sequences with other constants: A036412 (e), A036414 (phi), A036416 (Pi).

Table[Length@Complement[Range[n] - 1, Floor[n*FractionalPart[EulerGamma*Range[n]]]], {n, 81}] (* Ivan Neretin, Jan 23 2018 *)

A036412 Number of empty intervals when fractional_part(i*e) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 1, 1, 3, 1, 4, 4, 7, 5, 5, 6, 4, 4, 6, 7, 6, 8, 5, 2, 6, 4, 5, 3, 4, 3, 0, 3, 2, 0, 3, 3, 3, 0, 4, 4, 5, 6, 5, 6, 7, 8, 8, 8, 9, 8, 8, 7, 8, 8, 8, 9, 8, 8, 7, 6, 7, 6, 1, 5, 4, 4, 3, 2, 2, 0, 5, 4, 3, 5, 5, 6, 2, 8, 9, 9, 10, 11, 9, 11, 13, 16, 14, 16, 16, 17, 17, 18, 18, 20

Offset: 1

Eric W. Weisstein

nonn

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.

Cf. A036413 (positions of 0).
Cf. similar sequences with other constants: A036414 (phi), A036416 (Pi), A046157 (gamma).
Cf. A001113.

Table[Length@Complement[Range[n] - 1, Floor[n*FractionalPart[E*Range[n]]]], {n, 95}] (* Ivan Neretin, Jan 23 2018 *)

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

Original entry on oeis.org

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

Eric W. Weisstein

nonn

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

Cf. A036417 (positions of 0).

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

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

A036415 Values of k for which there are no empty intervals when fractional part(m*phi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040

Offset: 1

Eric W. Weisstein

The sequence contains the Fibonacci numbers A000045.
If fact, for all known terms with n > 10, a(n) = A000045(n-3). - Eric W. Weisstein, Apr 17 2024
No others terms with n <= 10^6. - Eric W. Weisstein, Apr 28 2024

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

Eric Weisstein's World of Mathematics, Equidistributed Sequence.
Eric Weisstein's World of Mathematics, Golden Ratio.

Cf. A000045, A036414.

With[{f = FractionalPart[GoldenRatio Range[1000]]}, Position[Table[Count[BinCounts[Take[f, n], {0., 1, 1/n}], 0], {n, Length[f]}], 0]] // Flatten (* Eric W. Weisstein, Apr 27 2024 *)

a(27)-a(29) from Sean A. Irvine, Oct 31 2020
a(30)-a(31) from Eric W. Weisstein, Apr 18-19 2024
a(32)-a(33) from Eric W. Weisstein, Apr 28 2024

cp's OEIS Frontend

A046157 Number of empty intervals when fractional_part(i*gamma) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions, where gamma is the Euler-Mascheroni constant.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A036412 Number of empty intervals when fractional_part(i*e) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A036415 Values of k for which there are no empty intervals when fractional part(m*phi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Extensions