|
%I #16 Jun 20 2021 19:18:13
%S 0,1,4,7,11,16,22,28,35,43,52,61,70,81,92,103,115,128,141,155,170,185,
%T 200,216,233,250,268,286,305,325,344,365,386,408,430,452,475,499,523,
%U 548,573,598,625,651,678,706,734,763,792,822,852,883,914,945,978,1010,1043,1077,1111,1145,1180,1216,1252,1288,1325
%N Floor of the arithmetic-geometric mean of n+n and n*n.
%C Arithmetic-geometric mean of n+n and n*n.
%C AGM of the sum and product of n and n.
%C a(n) = agm(A005843(n), A000290(n)).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_geometric_mean">Arithmetic-geometric mean</a>
%F a(n) = floor(agm(n+n,n*n)).
%e a(2) = floor(agm(2+2, 2*2)) = floor(agm(4, 4)) = 4.
%e a(5) = floor(agm(10.0, 25.0)) = floor(agm(17.5, 15.811388)) = floor(agm(16.655695, 16.634281)) = floor(agm(16.644987, 16.644983)) = floor(16.644987) = 16.
%t Table[Floor[ArithmeticGeometricMean[2n,n^2]],{n,0,70}] (* _Harvey P. Dale_, Aug 03 2014 *)
%o (Java) public class Agmnxn {
%o private static final double TOLERANCE = Math.pow(10, -4);
%o private static final long LENGTH = 250;
%o public static void main(String[] args) {
%o String series="";
%o long n=0;
%o while (series.length()<LENGTH) {
%o long x=(long) Math.floor(agm(n+n,n*n));
%o series+=x+",";
%o n++;
%o }
%o System.out.println(series);
%o }
%o private static double agm(double a, double g) {
%o return Math.abs(a-g)<TOLERANCE?a:agm((a+g)/2,Math.sqrt(a*g));
%o }
%o }
%Y Cf. A005843, A005843, A090852.
%K nonn,easy
%O 0,3
%A _John R Phelan_, Nov 11 2013
|
