A036417 Values of k for which there are no empty intervals when fractional part(m*Pi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

1, 6, 7, 106, 112, 113, 33102, 33215, 66317, 99532, 165849, 265381, 364913

Offset

1,2

Comments

Appears to include all the denominators of the convergents of Pi A002486. - Eric W. Weisstein, Apr 18 2024

No other terms with n <= 10^6. - Eric W. Weisstein, Apr 27 2024

Links

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Equidistributed Sequence.

Eric Weisstein's World of Mathematics, Pi.

Mathematica

With[{f = FractionalPart[Pi 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 *)

Crossrefs

Cf. A036416.

Cf. A002486 (denominators of the convergents of Pi).

Sequence in context: A223532 A041081 A041082 * A267255 A041357 A041829

Adjacent sequences: A036414 A036415 A036416 * A036418 A036419 A036420

Keyword

nonn,more,changed

Author

Eric W. Weisstein

Extensions

a(9)-a(10) from Sean A. Irvine, Oct 31 2020

a(11)-a(13) from Eric W. Weisstein, Apr 18-19 2024

Status

approved