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Numbers k such that the 5th power of k contains exactly 5 copies of each digit of k.
6

%I #27 Feb 29 2024 06:25:36

%S 961527834,7351062489,8105632794,8401253976,8731945026,9164072385,

%T 9238750614,9615278340,9847103256,72308154699,73510624890,81056327940,

%U 83170652949,83792140506,84012539760,87319450260,91602408573,91640723850,92387506140,96152783400,98471032560

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

%C 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 All terms are divisible by 9. First decimal digit of a term is 6 or larger. - _Chai Wah Wu_, Feb 27 2024

%H Chai Wah Wu, <a href="/A114261/b114261.txt">Table of n, a(n) for n = 1..26</a>

%e 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 (Python)

%o from itertools import count, islice

%o from sympy import integer_nthroot

%o def A114261_gen(): # generator of terms

%o for l in count(1):

%o a = integer_nthroot(10**(5*l-1),5)[0]

%o if (a9:=a%9):

%o a += 9-a9

%o for b in range(a,10**l,9):

%o if sorted(str(b)*5)==sorted(str(b**5)):

%o yield b

%o A114261_list = list(islice(A114261_gen(),5)) # _Chai Wah Wu_, Feb 27 2024

%Y Cf. A114258, A114259, A114260, A199632.

%K base,nonn

%O 1,1

%A _Giovanni Resta_, Nov 18 2005

%E a(8)-a(9) from _Ray Chandler_, Aug 23 2023

%E a(10)-a(21) from _Chai Wah Wu_, Feb 28 2024