Happy Primes

Square every digit of a positive integer $n$ and add the squares together. Do the same calculation again on the sum you get. If repeating this ever produces 1, then $n$ is a happy number.

700 is a happy number.

• $7^2 + 0^2 + 0^2 = 49$
• $4^2 + 9^2 = 97$
• $9^2 + 7^2 = 130$
• $1^2 + 3^2 + 0^2 = 10$
• $1^2 + 0^2 = 1$

2 is not a happy number.

• $2^2 = 4$
• $4^2 = 16$
• $1^2 + 6^2 = 37$
• $3^2 + 7^2 = 58$
• $5^2 + 8^2 = 89$
• $8^2 + 9^2 = 145$
• $1^2 + 4^2 + 5^2 = 42$
• $4^2 + 2^2 = 20$
• $2^2 + 0^2 = 4$
• $4^2 = 16$
• the calculation never ends.

A prime is a number with no divisors other than 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, ... are primes.

A happy prime is a number that is both prime and happy. 7, 13, 19, ... are happy primes.

Given $n$, write a program that finds every happy prime less than or equal to $n$.

The first line contains $n$ ($10 \le n \le 1\,000\,000$).

Print every happy prime less than or equal to $n$ in increasing order, one per line.