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 A036414 #21 Feb 16 2025 08:32:37
%S A036414 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,
%T A036414 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,
%U A036414 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
%N A036414 Number of empty intervals when fractional_part(i*phi) for i = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.
%D A036414 H. Steinhaus, Mathematical Snapshots, 3rd American ed. New York: Oxford University Press, pp. 48-49, 1983.
%H A036414 Ivan Neretin, <a href="/A036414/b036414.txt">Table of n, a(n) for n = 1..10000</a>
%H A036414 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EquidistributedSequence.html">Equidistributed Sequence</a>
%H A036414 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>
%t A036414 Table[Length@Complement[Range[n] - 1, Floor[n*FractionalPart[GoldenRatio*Range[n]]]], {n, 95}] (* _Ivan Neretin_, Jan 23 2018 *)
%t A036414 Table[Count[BinCounts[FractionalPart[GoldenRatio Range[n]], {0, 1, 1/n}], 0], {n, 95}] (* _Eric W. Weisstein_, Apr 17 2024 *)
%Y A036414 Cf. A036415 (positions of 0).
%Y A036414 Cf. similar sequences with other constants: A036412 (e), A036416 (Pi), A046157 (gamma).
%K A036414 nonn,look
%O A036414 1,9
%A A036414 _Eric W. Weisstein_