cp's OEIS Frontend

A352903 a(n) is the minimum number of steps required to construct a segment of length sqrt(n) in compass-and-straightedge construction.

%I A352903 #40 Jul 21 2023 11:09:37
%S A352903 1,5,3,2,6,5,5,5,3,5,5,4,5,5,5,3,6,5,6,6,5,6,6,5,4,6,5,5,6,6,6,6,5,6,
%T A352903 5,4,6,6,6,6,6,6,6,6,6,6,6,5,4,6,6,5,7,6,6,6,6,6,7,5,6,7,6,4,6,6,6,7,
%U A352903 6,6,7,6,6,7,6,6,6,6,6,6,5,7,7,5,7,7,7
%N A352903 a(n) is the minimum number of steps required to construct a segment of length sqrt(n) in compass-and-straightedge construction.
%C A352903 Compass-and-straightedge construction allows the use of only a straightedge (without scale) and a collapsing compass. A "step" consists of constructing a line or constructing a circle with a point as its center. Constructing an intersection uses 0 steps.
%C A352903 Given two points in the plane, separated by a unit distance, a segment of length sqrt(n) cannot be constructed in fewer than a(n) steps.
%C A352903 Proving that "a(2021) is not more than 10" was the 2021 Chinese Mathematical Olympiad's Problem 5. According to Y. Ai et al., it is known that a(2021) is not more than 8 and not less than 7 because the maximum k such that a(k)=6 is 1024.
%C A352903 The sequence greatest k such that a(k) = n begins at 1, 4, 16, 64, 256, 1024, 170569, ... - _Jinyuan Wang_, Jul 18 2023
%H A352903 Y. Ai et al., <a href="/A352903/a352903.pdf">Analysis of Questions and answers about the National Senior High School's Mathematical Olympiad in 2021 (Final)</a> (in Chinese).
%H A352903 L. Jin, <a href="https://mp.weixin.qq.com/s/94FQazqDwIX9g_7Aiobqyw">The generalized version of 2021 CMO Problem 5</a> (in Chinese).
%H A352903 Jinyuan Wang, <a href="/A352903/a352903.png">Illustration of initial terms</a>
%H A352903 Jinyuan Wang, <a href="/A352903/a352903.txt">PARI program</a>
%H A352903 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%K A352903 nonn,hard
%O A352903 1,2
%A A352903 _Yuda Chen_, Apr 07 2022
%E A352903 a(6) corrected by and more terms from _Jinyuan Wang_, Jul 17 2023