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

1,1

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A114258, A114259, A114260, A199632.

Sequence in context: A172605 A015394 A375644 * A321489 A168436 A168435

Adjacent sequences: A114258 A114259 A114260 * A114262 A114263 A114264

Keyword

base,nonn

Author

Giovanni Resta, Nov 18 2005

Extensions

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

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

Status

approved