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A371589
Smallest number m > 1 such that some permutation of the digits of m^n is a Fibonacci number.
1
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.
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
KEYWORD
nonn,base,more
AUTHOR
Chai Wah Wu, Mar 28 2024
EXTENSIONS
a(15)-a(23) from Bert Dobbelaere, Apr 10 2024
STATUS
approved