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

961527834, 7351062489, 8105632794, 8401253976, 8731945026, 9164072385, 9238750614, 9615278340, 9847103256, 72308154699, 73510624890, 81056327940, 83170652949, 83792140506, 84012539760, 87319450260, 91602408573, 91640723850, 92387506140, 96152783400, 98471032560

Offset: 1

Author

Giovanni Resta, Nov 18 2005

Keywords

• base
• nonn

Comments

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!

All terms are divisible by 9. First decimal digit of a term is 6 or larger. - Chai Wah Wu, Feb 27 2024

Examples

			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.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..26

Crossrefs

Cf. A114258, A114259, A114260, A199632.

Programs

Python

from itertools import count, islice
from sympy import integer_nthroot
def A114261_gen(): # generator of terms
    for l in count(1):
        a = integer_nthroot(10**(5*l-1),5)[0]
        if (a9:=a%9):
            a += 9-a9
        for b in range(a,10**l,9):
            if sorted(str(b)*5)==sorted(str(b**5)):
                yield b
A114261_list = list(islice(A114261_gen(),5)) # Chai Wah Wu, Feb 27 2024

Extensions

a(8)-a(9) from Ray Chandler, Aug 23 2023

a(10)-a(21) from Chai Wah Wu, Feb 28 2024