A371589 - OEIS

%I #22 Apr 11 2024 01:39:29

%S 2,12,2,19002,433153,472133,10064513,61054259,67878079,8152101,

%T 46077414,11395185,28556455,11730986,179311318,1542839498,443163383,

%U 2426412518,433059953,443302473,2654438078,2764480203,5945916934

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

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

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

%o (Python)

%o from itertools import count

%o from sympy import integer_nthroot

%o def A371589(n):

%o     a, b = 1, 2

%o     while True:

%o         s = sorted(str(b))

%o         m = int(''.join(s[::-1]))

%o         u = int(''.join(s))

%o         for i in count(max(2,integer_nthroot(u,n)[0])):

%o             if (k:=i**n) > m:

%o                 break

%o             t = sorted(str(k))

%o             if t == s:

%o                 return i

%o                 break

%o         a, b = b, a+b

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

%K nonn,base,more

%O 1,1

%A _Chai Wah Wu_, Mar 28 2024

%E a(15)-a(23) from _Bert Dobbelaere_, Apr 10 2024