A361826 - OEIS

%I #49 May 01 2023 18:06:26

%S 1,1,3,5,7,11,15,21,25,31,39,45,53,63,71,81,91,103,115,127,141,155,

%T 169,183,199,215,233,249,267,287,305,325,347,367,389,413,435,459,485,

%U 509,535,561,589,617,645,673,703,733,765,795,827,861,895,929,963,999,1035

%N a(n) is equal to the number of roots of the equation n*cos(x) = sqrt(x).

%C The number of roots of the equation is determined graphically. It is equal to the number of intersection points of two graphs: y = n*cos(x) and y = sqrt(x).

%H Nicolay Avilov, <a href="/A361826/a361826.jpg">Illustration for a(4)</a>.

%F Conjecture: a(n) = 2*floor(n^2/(2*Pi)) + 1.

%e a(4) = 5 because the equation 4*cos(x) = sqrt(x) has 5 roots. See link.

%Y Cf. A178832.

%K nonn

%O 1,3

%A _Nicolay Avilov_, Mar 27 2023