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A363905 Numbers whose square and cube taken together contain each decimal digit.

%I A363905 #20 Jun 28 2023 07:50:28
%S A363905 69,128,203,302,327,366,398,467,542,591,593,598,633,643,669,690,747,
%T A363905 759,903,923,943,1016,1018,1027,1028,1043,1086,1112,1182,1194,1199,
%U A363905 1233,1278,1280,1282,1328,1336,1364,1396,1419,1459,1463,1467,1472,1475
%N A363905 Numbers whose square and cube taken together contain each decimal digit.
%C A363905 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.
%C A363905 a(820) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice.
%H A363905 Robert G. Wilson v, <a href="/A363905/b363905.txt">Table of n, a(n) for n = 1..10000</a>
%H A363905 Harold Suarez, <a href="https://www.linkedin.com/feed/update/urn:li:activity:7073402002042417152">Interesting...</a>, Number Theory group on LinkedIn, June 2023.
%e A363905 69^2 = 4761, 69^3 = 328509, which together contain each digit 0-9 exactly once.
%t A363905 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 *)
%o A363905 (PARI) is(k)=#setunion(Set(digits(k^2)),Set(digits(k^3)))>9
%o A363905 select(is,[1..9999])
%o A363905 (Python)
%o A363905 from itertools import count, islice
%o A363905 def A363905_gen(startvalue=1): # generator of terms >= startvalue
%o A363905     return filter(lambda n:len(set(str(n**2))|set(str(n**3)))==10,count(max(startvalue,1)))
%o A363905 A363905_list = list(islice(A363905_gen(),20)) # _Chai Wah Wu_, Jun 27 2023
%Y A363905 Cf. A036744, A054038, A071519 and A156977 for "pandigital" squares.
%Y A363905 Cf. A119735: Numbers n such that every digit occurs at least once in n^3.
%K A363905 nonn,base,less
%O A363905 1,1
%A A363905 _M. F. Hasler_, Jun 27 2023