A371589 Smallest number m > 1 such that some permutation of the digits of m^n is a Fibonacci number.

2, 12, 2, 19002, 433153, 472133, 10064513, 61054259, 67878079, 8152101, 46077414, 11395185, 28556455, 11730986, 179311318, 1542839498, 443163383, 2426412518, 433059953, 443302473, 2654438078, 2764480203, 5945916934

Offset: 1

Author

Chai Wah Wu, Mar 28 2024

Keywords

• nonn
• base
• more

Comments

Unlike in A370071 or A371588, no leading 0's are allowed in m^n or the Fibonacci number.

Examples

			a(4) = 19002 since 19002^4 = 130375880664608016 and a permutation of its digits results in 160500643816367088, a Fibonacci number.
		

Crossrefs

Cf. A000045, A227875, A001597, A118715, A370071, A371588.

Programs

Python

from itertools import count
from sympy import integer_nthroot
def A371589(n):
    a, b = 1, 2
    while True:
        s = sorted(str(b))
        m = int(''.join(s[::-1]))
        u = int(''.join(s))
        for i in count(max(2,integer_nthroot(u,n)[0])):
            if (k:=i**n) > m:
                break
            t = sorted(str(k))
            if t == s:
                return i
                break
        a, b = b, a+b

Extensions

a(15)-a(23) from Bert Dobbelaere, Apr 10 2024