A364024 Least number whose square and cube, taken together, are pandigital n times.
69, 6534, 497375, 46839081, 4641856941, 464162827242, 46415911449392, 4641588990290676, 464158883559510629
Offset: 1
Examples
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.
Programs
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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]
Comments