A371588 - OEIS

%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