Getting the pointy hex coordinates of a hex region's center hex in this arrangement: https://www.redblobgames.com/grids/hexagons/#wraparound (Both the input and output are in "cube" hex coordinates. r is the radius of the regions.

gistfile1.js

const cubeCoordinatesToRegionCenter = (x, y, z, r) => {
  const centerX = x *  2 * r + x     +  r * z;
  const centerZ = z * -2 * r - z - x + -r * x;
  
  return [centerX, -centerX-centerZ, centerZ];
};