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#include <stdio.h>
 
int StarAndTriangleNumbers(int max); //protype
 
int main(int argc, char const *argv[]) {
 
  StarAndTriangleNumbers(10);
 
  return 0;
}
 
int StarAndTriangleNumbers(int max){
 
  int maxTriangles = max*10; //we need more triangle numbers than star numbers to check against 10 isnt specific would work with anything bigger than 5 probably
  int starNumbers[max]; //create an array to hold starnumbers
  int triangleNumbers[maxTriangles]; //creates an array to hold triangle numbers
 
  //create star numbers array
  for (int i = 1; i <= max; i++){
    starNumbers[i] = ( ( (6 * i) * ( i - 1) ) + 1 );
    // printf("star number %d is %d\n",i, starNumbers[i]);
  }
 
  //create triangle numbers array
  for (int i = 1; i <= maxTriangles; i++){
    int num = 0;
    for (int j = 1; j <= i; j++){
      num += j;
    }
    triangleNumbers[i] = num;
    // printf("triangle number %d is %d\n", i, triangleNumbers[i]);
  }
 
  int matches[max]; //hold indcies of which ever star number matches a triangle numbers
  int y = 0;
 
  //simple binary search algorithm.
  for (int i = 1; i <= max; i++){
    for (int j = 1; j < maxTriangles; j++){
      if(starNumbers[i] == triangleNumbers[j]){
        matches[y] = i;
        y++;
      }
    }
  }
 
  //print out the numbers
  for (int i = 0; i < (y - 1); i++) {
    printf("%d,", starNumbers[matches[i]]);
  }
  printf("%d\n", starNumbers[matches[y-1]]);
 
  return 0;
 
}