Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Jun 28 2023 07:50:28
%S 69,128,203,302,327,366,398,467,542,591,593,598,633,643,669,690,747,
%T 759,903,923,943,1016,1018,1027,1028,1043,1086,1112,1182,1194,1199,
%U 1233,1278,1280,1282,1328,1336,1364,1396,1419,1459,1463,1467,1472,1475
%N Numbers whose square and cube taken together contain each decimal digit.
%C 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 a(820) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice.
%H Robert G. Wilson v, <a href="/A363905/b363905.txt">Table of n, a(n) for n = 1..10000</a>
%H Harold Suarez, <a href="https://www.linkedin.com/feed/update/urn:li:activity:7073402002042417152">Interesting...</a>, Number Theory group on LinkedIn, June 2023.
%e 69^2 = 4761, 69^3 = 328509, which together contain each digit 0-9 exactly once.
%t 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 (PARI) is(k)=#setunion(Set(digits(k^2)),Set(digits(k^3)))>9
%o select(is,[1..9999])
%o (Python)
%o from itertools import count, islice
%o def A363905_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda n:len(set(str(n**2))|set(str(n**3)))==10,count(max(startvalue,1)))
%o A363905_list = list(islice(A363905_gen(),20)) # _Chai Wah Wu_, Jun 27 2023
%Y Cf. A036744, A054038, A071519 and A156977 for "pandigital" squares.
%Y Cf. A119735: Numbers n such that every digit occurs at least once in n^3.
%K nonn,base,less
%O 1,1
%A _M. F. Hasler_, Jun 27 2023