OFFSET
1,1
COMMENTS
The first term, a(1) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice.
Presumably a(n) ~ A363905(n) ~ n. - Charles R Greathouse IV, Jul 03 2023
LINKS
Harold Suarez, Interesting..., Number Theory group on LinkedIn, (capture of the original post), June 2023
EXAMPLE
6534^2 = 42693156, 6534^3 = 278957081304, which together contain each digit 0-9 exactly twice.
PROG
(PARI) is(n)=#Set(n=concat(digits(n^2), digits(n^3)))>9&&(n=vecsort(n))[#n-1]==9&&!n[2]&&!for(i=3, #n-2, n[i]>n[i-1]&&n[i]<n[i+1]&&return)
select(is, [2111..39999])
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
M. F. Hasler, Jun 27 2023
STATUS
approved