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A085453
Numbers n such that n^2 and n^3 together use only distinct digits.
0
2, 3, 8, 9, 24, 69
OFFSET
1,1
COMMENTS
There are only six such numbers (in base 10). Numbers with distinct digits in A010784. Primes with distinct digits in A029743. The case n and n^2 (exactly 22 numbers) in A059930. The case n and prime[n] (exactly 101 numbers) in A085451.
EXAMPLE
69 is (the last) term because 69^2=4761 and 69^3=328509 together use all 10 distinct digits.
MATHEMATICA
bb = {}; Do[idpn = IntegerDigits[n^3]; idn = IntegerDigits[n^2]; If[Length[idn] + Length[idpn] == Length[Union[idn, idpn]], bb = {bb, n}], {n, 1, 10000}]; Flatten[bb]
CROSSREFS
KEYWORD
fini,full,nonn,base
AUTHOR
Zak Seidov, Jul 01 2003
STATUS
approved