A326406

import java.lang.Math;

class A326406{
    public static void main(String[] args){
    int length = 100;                                               //length of sequence
    int side = (int) (Math.ceil((Math.sqrt(8*length+1)-1)/2)+1);
    int[][] grid = new int[side][side];
    fillGrid(grid);
    //display(grid);
    int[][] marked = markMines(grid);
    int[][] transf = transform(marked);
    read(length, transf);
    }

    static int[] coordinates(int n){
        int[] output = new int[2];
        int lower = (int) (Math.ceil((Math.sqrt(8*n+1)-1)/2)-1);
        int max = (lower+2)*(lower+1)/2;
        int reminder = max - n;

        if(lower%2==1){
            output[0]= lower - reminder;
            output[1]= reminder;
        } else {
            output[1]= lower - reminder;
            output[0]= reminder;
        }


        //System.out.println(n+"   " + lower + "  " + reminder + "  " + output[0]+ "   "+output[1]);
        return output;
    }

    static void fillGrid(int[][] grid){
        grid[0][0] = 1;
        for (int i = 2; i < grid.length*grid.length+1 ; i++){
            int[] position = coordinates(i);
            if (position[0] > -1 && position[1]>-1 && position[0] < grid.length && position[1] < grid.length) {grid[position[0]][position[1]]=i;}
        }
    }

    static int[][] markMines(int[][] grid){
        int[][] output = new int[grid.length][grid.length];
        for(int i = 0; i < grid.length; i++){
            for(int j = 0; j < grid.length; j++){
                if (isPrime(grid[i][j])){
                    output[i][j] = -1;
                } else {
                    output[i][j] = grid[i][j];
                }
            }
        }
        return output;
    }

    static int checkMine(int i, int j, int[][] grid){
        if (grid[i][j] == -1) {return 1;}
        else {return 0;}
    }

    static int[][] transform(int[][] grid){
        int[][] output = new int[grid.length][grid.length];

        for(int i = 0; i < grid.length; i++){
            for(int j = 0; j < grid.length; j++){
                if (checkMine(i,j,grid)==1){output[i][j]=-1;}
                else {
                    for (int k = -1; k<2;k++){
                        for (int l = -1; l<2;l++){
                            if ((i+k>-1) && (j+l>-1) && (i+k<grid.length) && (j+l<grid.length)) {output[i][j]=output[i][j]+checkMine(i+k,j+l,grid);}
                        }
                    }
                }
            }
        }
        return output;
    }

    static boolean isPrime(int n){
        if (n==1){return false;}
        if (n==2){return true;}
        if (n>2){
            if (n%2==0) {return false;}
            else{
                for(int i=3; i*i < n+1 ;i++){
                    if (n%i == 0) {return false;}
                }
            }
        }
        return true;
    }

    static void display(int[][] array){
        for (int i = 0; i< array.length; i++){
            for (int j = 0; j< array[0].length; j++){
                System.out.print(array[i][j]+"\t");
            }
        System.out.println();
        }
    }

    static void read(int n, int[][] grid){
        for (int i = 1; i< n+1; i++){
            System.out.println(i+ "  " + grid[coordinates(i)[0]][coordinates(i)[1]]);
        }
    }
}