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%I #21 Mar 30 2024 15:56:41
%S 2,144,8,610,5358359254990966640871840,
%T 68330027629092351019822533679447,
%U 15156039800290547036315704478931467953361427680642,23770696554372451866815101694984845480039225387896643963981,119447720249892581203851665820676436622934188700177088360
%N Smallest Fibonacci number > 1 such that some permutation of its digits is a perfect n-th power.
%C Subsequence of A370071 after reordering (as the sequence is not monotonic; e.g., a(2) > a(3) and a(8) > a(9)). Leading 0 digits are allowed in the perfect power. For example, a(4) = 610 since 016 = 2^4. (If leading 0 digits were not allowed, a(4) would be 160500643816367088.)
%H Chai Wah Wu, <a href="/A371588/b371588.txt">Table of n, a(n) for n = 1..16</a>
%e a(1) = 2 since 2 = 2^1.
%e a(2) = 144 since 144 = 12^2.
%e a(3) = 8 since 8 = 2^3.
%e a(4) = 610 since 016 = 2^4.
%e a(5) = 5358359254990966640871840 since 0735948608251696955804943 = 59343^5
%e a(6) = 68330027629092351019822533679447 since 00059398947526192142327360782336 = 62464^6.
%o (Python)
%o from itertools import count
%o from sympy import integer_nthroot
%o def A371588(n):
%o a, b = 1, 2
%o while True:
%o s = sorted(str(b))
%o l = len(s)
%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 ['0']*(l-len(t))+t == s:
%o return b
%o break
%o a, b = b, a+b
%Y Cf. A000045, A227875, A001597, A118715, A370071.
%K nonn,base,more
%O 1,1
%A _Chai Wah Wu_, Mar 28 2024
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