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

1,1

Comments

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

Links

Table of n, a(n) for n=1..23.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A246737 A012626 A012629 * A082827 A290100 A302389

Adjacent sequences: A371586 A371587 A371588 * A371590 A371591 A371592

Keyword

nonn,base,more

Author

Chai Wah Wu, Mar 28 2024

Extensions

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

Status

approved