OFFSET
1,1
EXAMPLE
a(1) is 69 since 69^2 = 4761 and 69^3 = 328509; together they include each of the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} exactly once;
a(2) is 6534 since 6534^2 = 42693156 and 6534^3 = 278957081304; together they include each decimal digit exactly twice;
a(3) is 497375 since 497375^2 = 247381890625 and 497375^3 = 123041567849609375; together they include each decimal digit exactly three times; etc.
MATHEMATICA
f[n_] := Block[{k = Floor[10^(2n-1/3)]}, While[ !MemberQ[{0, 3, 6, 8}, Mod[k, 9]] || Length@ Union[ Count[ Sort[ Join[ IntegerDigits[k^2], IntegerDigits[k^3]]], #] & /@ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}] > 1, k++]; k]
CROSSREFS
KEYWORD
base,more,nonn
AUTHOR
Robert G. Wilson v, Jul 01 2023
STATUS
approved