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A114261 Numbers k such that the 5th power of k contains exactly 5 copies of each digit of k.

%I A114261 #27 Feb 29 2024 06:25:36
%S A114261 961527834,7351062489,8105632794,8401253976,8731945026,9164072385,
%T A114261 9238750614,9615278340,9847103256,72308154699,73510624890,81056327940,
%U A114261 83170652949,83792140506,84012539760,87319450260,91602408573,91640723850,92387506140,96152783400,98471032560
%N A114261 Numbers k such that the 5th power of k contains exactly 5 copies of each digit of k.
%C A114261 Some of the early terms of the sequence are also pandigital, i.e. they contain all the 10 digits once. This is probably accidental, but quite curious!
%C A114261 All terms are divisible by 9. First decimal digit of a term is 6 or larger. - _Chai Wah Wu_, Feb 27 2024
%H A114261 Chai Wah Wu, <a href="/A114261/b114261.txt">Table of n, a(n) for n = 1..26</a>
%e A114261 E.g. 961527834 is in the sequence since its 5th power 821881685441327565743977956591832631269739424 contains five 9's, five 6's, five 1's and so on.
%o A114261 (Python)
%o A114261 from itertools import count, islice
%o A114261 from sympy import integer_nthroot
%o A114261 def A114261_gen(): # generator of terms
%o A114261     for l in count(1):
%o A114261         a = integer_nthroot(10**(5*l-1),5)[0]
%o A114261         if (a9:=a%9):
%o A114261             a += 9-a9
%o A114261         for b in range(a,10**l,9):
%o A114261             if sorted(str(b)*5)==sorted(str(b**5)):
%o A114261                 yield b
%o A114261 A114261_list = list(islice(A114261_gen(),5)) # _Chai Wah Wu_, Feb 27 2024
%Y A114261 Cf. A114258, A114259, A114260, A199632.
%K A114261 base,nonn
%O A114261 1,1
%A A114261 _Giovanni Resta_, Nov 18 2005
%E A114261 a(8)-a(9) from _Ray Chandler_, Aug 23 2023
%E A114261 a(10)-a(21) from _Chai Wah Wu_, Feb 28 2024