OFFSET
1,1
COMMENTS
The first term, a(1) = 69, is the only number for which the square and the cube together contain each decimal digit 0 to 9 exactly once.
a(820) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Harold Suarez, Interesting..., Number Theory group on LinkedIn, June 2023.
EXAMPLE
69^2 = 4761, 69^3 = 328509, which together contain each digit 0-9 exactly once.
MATHEMATICA
fQ[n_] := Union[ Join[ IntegerDigits[n^2], IntegerDigits[n^3]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; Select[Range@1500, fQ] (* Robert G. Wilson v, Jun 27 2023 *)
PROG
(PARI) is(k)=#setunion(Set(digits(k^2)), Set(digits(k^3)))>9
select(is, [1..9999])
(Python)
from itertools import count, islice
def A363905_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:len(set(str(n**2))|set(str(n**3)))==10, count(max(startvalue, 1)))
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
M. F. Hasler, Jun 27 2023
STATUS
approved