A036415 - OEIS

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.

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

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OFFSET

1,2

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..33.

Eric Weisstein's World of Mathematics, Equidistributed Sequence.

Eric Weisstein's World of Mathematics, Golden Ratio.

MATHEMATICA

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 *)

CROSSREFS

Cf. A000045, A036414.

Sequence in context: A241089 A186445 A080078 * A054961 A086736 A175773

Adjacent sequences: A036412 A036413 A036414 * A036416 A036417 A036418

KEYWORD

nonn,more

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

STATUS

approved