A046519 Least n-digit 'happy' prime.

7, 13, 103, 1009, 10009, 100003, 1000003, 10000121, 100000039, 1000000009, 10000000033, 100000000003, 1000000000039, 10000000000411, 100000000000067, 1000000000000487, 10000000000000481, 100000000000000003

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Comments

Values found by Harvey Heinz and Jud McCranie.

References

• R. K. Guy, Unsolved Problems Number Theory, Sect. E34.

Links

• Bo Gyu Jeong, Table of n, a(n) for n = 1..50
• C. Rivera, Related puzzle page
• Eric Weisstein's World of Mathematics, Happy Number

Crossrefs

Cf. A007770, A035497.

Programs

Python

from sympy import nextprime
def A046519(n):
    m = 10**(n-1)
    while (m:=nextprime(m)):
        k = m
        while k not in {1,37,58,89,145,42,20,4,16}:
            k = sum((0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[ord(d)-48] for d in str(k))
        if k == 1:
            return m # Chai Wah Wu, Aug 02 2023