This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036415 #48 Feb 16 2025 08:32:37
%S A036415 1,2,3,4,5,6,8,10,13,16,21,34,55,89,144,233,377,610,987,1597,2584,
%T A036415 4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,
%U A036415 832040
%N 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.
%C A036415 The sequence contains the Fibonacci numbers A000045.
%C A036415 If fact, for all known terms with n > 10, a(n) = A000045(n-3). - _Eric W. Weisstein_, Apr 17 2024
%C A036415 No others terms with n <= 10^6. - _Eric W. Weisstein_, Apr 28 2024
%D A036415 H. Steinhaus, Mathematical Snapshots, 3rd American ed., New York: Oxford University Press, pp. 48-49, 1983.
%H A036415 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EquidistributedSequence.html">Equidistributed Sequence</a>.
%H A036415 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>.
%t A036415 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 *)
%Y A036415 Cf. A000045, A036414.
%K A036415 nonn,more
%O A036415 1,2
%A A036415 _Eric W. Weisstein_
%E A036415 a(27)-a(29) from _Sean A. Irvine_, Oct 31 2020
%E A036415 a(30)-a(31) from _Eric W. Weisstein_, Apr 18-19 2024
%E A036415 a(32)-a(33) from _Eric W. Weisstein_, Apr 28 2024