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%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
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