Here is a C version code, I think it's easy to rewrite it in other language based on the logical.
int isConsecutive(int *array, int length) {
int i = 1;
for (; i < length; i++) {
if (array[i] != array[i - 1] + 1)
return 0; //which means false and it's not a consecutive list
}
return 1;
}