Problem 387
Harshad Numbers
A Harshad or Niven number is a number that is divisible by the sum of its digits.
201 is a Harshad number because it is divisible by 3 (the sum of its digits).
When we truncate the last digit from 201, we get 20, which is a Harshad number.
When we truncate the last digit from 20, we get 2, which is also a Harshad number.
Let’s call a Harshad number that, while recursively truncating the last digit, always results in a Harshad number a right truncatable Harshad number.
Also:
201/3=67 which is prime.
Let’s call a Harshad number that, when divided by the sum of its digits, results in a prime a strong Harshad number.
Now take the number 2011 which is prime.
When we truncate the last digit from it we get 201, a strong Harshad number that is also right truncatable.
Let’s call such primes strong, right truncatable Harshad primes.
You are given that the sum of the strong, right truncatable Harshad primes less than 10000 is 90619.
Find the sum of the strong, right truncatable Harshad primes less than 1014.
哈沙德数
能够被其各位数字和整除的数被称为哈沙德数或奈文数。
201是一个哈沙德数，因为它能被3整除（其各位数字和是3）。
如果我们截去201的最后一位数字，我们得到20，同样是一个哈沙德数。
如果我们截去20的最后一位数字，我们得到2，仍然是一个哈沙德数。
如果一个哈沙德数不断截去最后一位数字的结果始终是哈沙德数，我们称之为可右截哈沙德数。
此外：
201/3=67是一个素数。
如果一个哈沙德数被其各位数字除的结果是一个素数，我们称之为强哈沙德数。
现在我们取素数2011。
如果我们截去2011的最后一位数字，我们得到201，一个可右截的强哈沙德数。
我们称这样的素数为可右截强哈沙德素数。
已知所有小于10000的可右截强哈沙德素数之和为90619。
求所有小于1014的可右截强哈沙德素数之和。